You are awesome! I am teaching my daughter perpendicular lines and use your videos as a reference guide when I am setting up my lesson plan with her. I love teaching algebra, but have never been a graphing lines person, but your breakdown helps me be a more effective teacher for her and she’s totally getting it!
COMPREHENSION #2 SOLUTION First line, y = -2x + 5 New line is perpendicular, so the slope (the x coefficient) must be the opposite reciprocal of -2. Flip the term and flip the sign: Slope = 1/2. But we don't know the 'b' value: y = (1/2)x + b To calculate the b value, substitute the coordinates of the point (1,-1), where x = 1 and y = -1: -1 = (1/2)(1) + b Flip the equation around and subtract (1/2)(1) from both sides: ∴ b = -1 - (1/2)(1) ∴ b = -1 - 1/2 ∴ b = -3/2 Substitute b value into the new line's equation: ∴ y = (1/2)x - 3/2 (brackets shown to be clear that x multiples 1/2 and not just the 2 on the bottom, cuz I'm writing on one line)
∴ b = -1 - (1/2)(1) ∴ b = -1 - 1/2 ∴ b = -3/2 should be the y -1 become positive 1 when u move in the right side? and is this the concept u did -1 x 2 = -2 then -2 -1 = -3 that is why it become -3/2? if im correct thank u so much im having problem in the no.2 solution
@@romyow6326 When I went from -1 = (1/2)(1) + b to b = -1 - (1/2)(1) I subtracted (1/2)(1) from both sides and then just swapped the whole sides of the equation around. Later, 1 is the same as 2/2, so -1 - 1/2 is the same as -2/2 - 1/2, which equals -3/2.
tried it and failed and was about to tear my hair out not getting it. im supposed to know this stuff but i have memory issues and its so embarassing asking a for help again especially a nice teacher who always gives 110%. thank you so much
The right side, i was found this trick by my self from the past equation of per slope intercept form when i try to solve fraction y=1/2 x + 1 (Here just example from other equation) When y1 = 1/2 (1) +1 . U can't multiply just 1, every integer like inside (1) is the same as 1/1 even if it's 5 9 or else must have run or divide by 1 like 5/1,9/1 So then we found y1 = 1/2 * 1/1 then we cross multiply it! It becomes 2/1 and the 2 in the lcm of the denominator is [1*2] which is equals to 2 so it becomes 2/2. Back to our problem, -1 = 1/2 (1) - b -1 = 1/2 * 1/1 - b -1 = 2/2 - b -2/2 -1/1 = b (lcm of 2 and 1 is 2) -3/2 = b @@apspencer6685
My math teacher told me to stick to my grade level while I was in the process of watching these videos! I will continue to watch your beautiful videos professor.
COMPREHENSION #1 SOLUTION First line, y = 4x -1 New line is parallel, so the slope (the x coefficient) must be the same, 4. But we don't know the 'b' value: y = 4x + b To calculate the b value, substitute the coordinates of the point (4, 9), where x = 4 and y = 9: 9 = 4(4) + b Flip the equation around and subtract 4(4) from both sides: ∴ b = 9 - 4(4) ∴ b = 9 - 16 ∴ b = -7 Substitute b value into the new line's equation: ∴ y = 4x - 7
I have a question. So you said I have to plug in whatever the points were given to y=mx+b, but why do we do that. I dont get it because isnt b in y=mx+b a y value in the graph?
So if someone wants to know if changing sign for slopes of a perpendicular is true or not, it's true I personally verified it just now I made a graph with scale, coordinates I got for both lines were (3, 0) & (0, 3) and for perpendicular lines it was (3, 3) & (0, 0) solve for slope you will get -1 and +1
Checking Comprehension SPOILERS!! I wrote down my answer for the second question as y = 1/2x - 1 1/2. Is this correct? Should I write down my answers in a specific way?
It’s correct but it’s better if you write it as -3/2 instead of -1 1/2. Since this is just a small linear equation it’s not messy, but on larger or more complicated expressions, improper fractions ( like 3/2 ) are neater and easier to work with. It is something in algebra you’ll have to get used to. I hope this answered your question, have a nice day.
I have a question! In comprehension 1 my answer is: y= (-1/4)x + 10. This is what I did... Real Problem: y = 4x - 1 Line: (4,9) Solution I did: y = (-1/4)x + b 9 = (-1/4)(4) + b 9 = (-4/4) + b 9 = -1 + b 9 + 1 = b 10 = b Therefore: y = (-1/4)x + 10 Where did I do wrong? I am stuck for minutes now😭😭😭
the fact that i'm preparing for my master degree and i came back to watch your videos about math i really wished to know your channel before when i was stucking with math
The funny part is when I graph y=-2x+5 and y=(1/2)x-(3/2) they don’t look perpendicular on my calculator. I know the math is good though. Weird stuff. Edit: It had to do with the different scales on my x and y-axis. When I checked it on an a web app the graphs were perfectly perpendicular.
for the first checking comprehension question, I got the y intercept equal to positive 7. so you plug in the values and get 9=16-b, and you subtract 16 to get -7=-b, which would make b=7 since both negatives cancel out. So does that mean whenever I am doing this, I MUST start out in slope intercept form which would lend a positive value to the y intercept always, despite the example in question 1 lending a negative value to the y intercept in the question?
Form doesn't matter, they are interchangable - in maths it's always only the question if you have all the minimally needed information to use a certain set of rules/forms/etc.. You just made the error of using y = mx - b instead of y = mx + b (probably because you confused b = -1 for a change in the sign of b... [edit] Just read the first line equation as y = 4x + (-1), that should clarify it additionally [/edit]). So 9 = 16 - b is where you went wrong, that should be 9 = 16 + b --> -7 = b (or b = -7)
Flip the term/ flip the sign , that's the secret , but I dont understand the flip ..show me specifically what this is .... ...U.S.MARINE... ..I.MUST SOLVE THIS ...OVER...
![ปฏิเสธไม่ไหว (Crush on you) - LIPTA feat. No One Else [Official MV]](http://i.ytimg.com/vi/NBw1jF342vw/mqdefault.jpg)
Thank you teacher. This is so helpful.
Oh well you weren't concentrating in your school...no problem ..Sir Dave is here ;)
bad teachers dont help!!!!
Even u werent thats why u reached her so shut up fam
True@@tfr
or they only teach you it for 5 minutes a few months ago and they expect to take a full test about it
You are awesome! I am teaching my daughter perpendicular lines and use your videos as a reference guide when I am setting up my lesson plan with her. I love teaching algebra, but have never been a graphing lines person, but your breakdown helps me be a more effective teacher for her and she’s totally getting it!
COMPREHENSION #2 SOLUTION
First line, y = -2x + 5
New line is perpendicular, so the slope (the x coefficient) must be the opposite reciprocal of -2. Flip the term and flip the sign: Slope = 1/2. But we don't know the 'b' value:
y = (1/2)x + b
To calculate the b value, substitute the coordinates of the point (1,-1), where x = 1 and y = -1:
-1 = (1/2)(1) + b
Flip the equation around and subtract (1/2)(1) from both sides:
∴ b = -1 - (1/2)(1)
∴ b = -1 - 1/2
∴ b = -3/2
Substitute b value into the new line's equation:
∴ y = (1/2)x - 3/2 (brackets shown to be clear that x multiples 1/2 and not just the 2 on the bottom, cuz I'm writing on one line)
∴ b = -1 - (1/2)(1)
∴ b = -1 - 1/2
∴ b = -3/2
should be the y -1 become positive 1 when u move in the right side?
and is this the concept u did -1 x 2 = -2 then -2 -1 = -3 that is why it become -3/2?
if im correct thank u so much im having problem in the no.2 solution
@@romyow6326 When I went from -1 = (1/2)(1) + b to b = -1 - (1/2)(1) I subtracted (1/2)(1) from both sides and then just swapped the whole sides of the equation around. Later, 1 is the same as 2/2, so -1 - 1/2 is the same as -2/2 - 1/2, which equals -3/2.
tried it and failed and was about to tear my hair out not getting it. im supposed to know this stuff but i have memory issues and its so embarassing asking a for help again especially a nice teacher who always gives 110%. thank you so much
The right side, i was found this trick by my self from the past equation of per slope intercept form when i try to solve fraction y=1/2 x + 1
(Here just example from other equation)
When y1 = 1/2 (1) +1 . U can't multiply just 1, every integer like inside (1) is the same as 1/1 even if it's 5 9 or else must have run or divide by 1 like 5/1,9/1
So then we found y1 = 1/2 * 1/1 then we cross multiply it! It becomes 2/1 and the 2 in the lcm of the denominator is [1*2] which is equals to 2 so it becomes 2/2.
Back to our problem, -1 = 1/2 (1) - b
-1 = 1/2 * 1/1 - b
-1 = 2/2 - b
-2/2 -1/1 = b (lcm of 2 and 1 is 2)
-3/2 = b
@@apspencer6685
this now makes sence thanks!
My math teacher told me to stick to my grade level while I was in the process of watching these videos! I will continue to watch your beautiful videos professor.
I love the intro I've been watching the playlist for revision and I never skip the intro...love it😂
I forgot everything i learn in school thanks proffesor
instaBlaster
Same here
the best class ever learnt thanks
CJ CREATIONS maybe u need some English to... u said “learnt” instead of learned 😂😂
@@RAPTORTATECHANNEL stfu
@@RAPTORTATECHANNEL and you used the wrong to it’s too, you need to learn how to type correctly :)
Great sessions
Thank you so much professor
This is so helpful
thank you this helped me complete an aleks topic
Thanks So much sir.Tommorow I have GED Maths Exam.
Thanks Pofessor Dave
Dude im from poland and I understood more that any polish person could thanks dude
This was extremely helpful🙃 thank you
I just donnow how to thank u for this great vid , thanks a lot mr Dave 😊
Bro thanks so much I had algebra homework and didn’t understand how to do the problem you’re awesome
Thanks bro
Thank you sir
Thank you man 👨
Thank you❤
the best teacher, making everything that seems hard so easy
Sir the best pls upload more math chapters
Reading is fundamental even in Mathematics
indeed dave knows *almost* everything
useful info. man
thanks for making this video
Thnx u were great help :)
Who else is on their way to their math exam learning these graphs for the first time. I only had a month to learn biology, math, english don't judge!
COMPREHENSION #1 SOLUTION
First line, y = 4x -1
New line is parallel, so the slope (the x coefficient) must be the same, 4. But we don't know the 'b' value:
y = 4x + b
To calculate the b value, substitute the coordinates of the point (4, 9), where x = 4 and y = 9:
9 = 4(4) + b
Flip the equation around and subtract 4(4) from both sides:
∴ b = 9 - 4(4)
∴ b = 9 - 16
∴ b = -7
Substitute b value into the new line's equation:
∴ y = 4x - 7
Quick question, why didn't you change 4 to (-1/4)?
@@ystyphnboth3610 That's for perpendicular lines (lines at 90 degrees to each other), but comprehension 1 is about parallel lines.
I have a question. So you said I have to plug in whatever the points were given to y=mx+b, but why do we do that. I dont get it because isnt b in y=mx+b a y value in the graph?
So if someone wants to know if changing sign for slopes of a perpendicular is true or not, it's true I personally verified it just now I made a graph with scale, coordinates I got for both lines were (3, 0) & (0, 3) and for perpendicular lines it was (3, 3) & (0, 0) solve for slope you will get -1 and +1
Also I verified with tan theta = P/B that my line is at an 90° angle from the first line
Still lost lol
This helped me so much
You are so much better than khan academy!
Nice meeting u sir
Danke du bist der beste
Online class is waving
Really nice work done! Solved my all queries. Thanks a lot. Keep up the good work ! :-)
Checking Comprehension SPOILERS!!
I wrote down my answer for the second question as y = 1/2x - 1 1/2. Is this correct?
Should I write down my answers in a specific way?
It’s correct but it’s better if you write it as -3/2 instead of -1 1/2. Since this is just a small linear equation it’s not messy, but on larger or more complicated expressions, improper fractions ( like 3/2 ) are neater and easier to work with. It is something in algebra you’ll have to get used to. I hope this answered your question, have a nice day.
I have a question! In comprehension 1 my answer is:
y= (-1/4)x + 10.
This is what I did...
Real Problem:
y = 4x - 1
Line: (4,9)
Solution I did:
y = (-1/4)x + b
9 = (-1/4)(4) + b
9 = (-4/4) + b
9 = -1 + b
9 + 1 = b
10 = b
Therefore:
y = (-1/4)x + 10
Where did I do wrong? I am stuck for minutes now😭😭😭
The 9 would be the b in y=mx+b
Not the y because the y is the result for example y=5+2 aka y=7
@@spidercat5317I finally understood why. The problem is asking for parallel line equation and not perpendicular hahahah
Tysm I was gonna fail an exam
Good luck
Can someone please solve that 1st comprehension... cuz I'm getting a different answer..
3:03
yay
Helpful, thank you
me in class learning ): learning hear (:
What is the "b" referring to?
y-intercept
When I see slope m = a/b, then a perpendicular slope is -(b/a).
does y or x comes first
i'm not sure what you mean
x is first, then y. (4 , 5) would be x=4 y=5
x comes first
@@ProfessorDaveExplainsevere single math teacher 😂😂😂
POV:LEGENDS WATCHING IT ONE DAY BEFORE THEIR EXAM
the right angle is NOT a right angle
THANK YOU GOD!!
the fact that i'm preparing for my master degree and i came back to watch your videos about math i really wished to know your channel before when i was stucking with math
❤❤❤❤
LMAO LOOK AT YOUR FACE IN THE INTRO
I ALWAYS and I do mean ALWAYS confuse inverse with reciprocal.
How did he get 8???
subtract 12 from both sides
Wait what level is this? I was searching it Bc I saw it on my nwea test..
algebra 1, usually around 8th grade give or take a year depending on track
The funny part is when I graph y=-2x+5 and y=(1/2)x-(3/2) they don’t look perpendicular on my calculator. I know the math is good though. Weird stuff.
Edit: It had to do with the different scales on my x and y-axis. When I checked it on an a web app the graphs were perfectly perpendicular.
when I do the first one I get y=4x+1 the second I get y=2x-3 so I'm confused
y= 4x-1
y=4x + b
9= 4(4) + b
9-16 = b
-7= b
y= -2x + 5
y= 1/2x + b
-1= 1/2 (1) + b
-1- 1/2 = b
-3/2 = b
I hope this helps. Have a nice day !
Where tf did he get -8???
Timestamp plz? I don't know where u are talking about..
@@naomigwolfe8112 Around 2:44
@@ilulu09 ohh thank u
he subtracted 12 from each side.
for the first checking comprehension question, I got the y intercept equal to positive 7. so you plug in the values and get 9=16-b, and you subtract 16 to get -7=-b, which would make b=7 since both negatives cancel out. So does that mean whenever I am doing this, I MUST start out in slope intercept form which would lend a positive value to the y intercept always, despite the example in question 1 lending a negative value to the y intercept in the question?
Form doesn't matter, they are interchangable - in maths it's always only the question if you have all the minimally needed information to use a certain set of rules/forms/etc..
You just made the error of using y = mx - b instead of y = mx + b (probably because you confused b = -1 for a change in the sign of b... [edit] Just read the first line equation as y = 4x + (-1), that should clarify it additionally [/edit]).
So 9 = 16 - b is where you went wrong, that should be 9 = 16 + b --> -7 = b (or b = -7)
thx !@@Teiwaz111
What is bro saying
this is the clearest video i found on this topic 💀
@@OwenDinwiddiemy man really mewing and silencing us In ❤
thank you for the video. just to check: for finding the opposite reciprocal do you divide 1 by the gradient or -1 by the gradient?
-1 over the slope will give you the opposite reciprocal!
Professor Dave Explains wtf
@@lordgaming5402 haters hate
This s**ts confusing ngl
Flip the term/ flip the sign , that's the secret , but I dont understand the flip ..show me specifically what this is ....
...U.S.MARINE...
..I.MUST SOLVE THIS ...OVER...
bad
tfffffffffffffffffff 3lik
Haha lbnene
Rakz 🤣🤣
thanks professor dave 💀