Graphing a linear inequality by the x and y intercepts

👉 Learn how to graph linear inequalities written in standard form. Linear inequalities are graphed the same way as linear equations, the only difference being that one side of the line that satisfies the inequality is shaded. Also broken line (dashes) is used when the linear inequality is 'excluded' (when less than or greater than is used) and a solid line is used when the inequality is 'included' (when greater than or equal to OR less than or equal to is used).
To graph a linear inequality written in standard form, we first determine the slope and the y-intercept by rewriting the linear inequality in slope intercept form, we then plot the y-intercept and using the slope, we can determine the rise and the run of the required line and then be able to plot the next point from the y-intercept. We then draw a straight line passing through the two plotted points.
Alternatively, we can determine the x-intercept and the y-intercept of the standard form linear inequality by substituting y = 0, then solve for x and substituting x = 0, then solve for y respectively. Recall that the x-intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0. After obtaining the values of the x-intercept and the y-intercept, we plot the points on the coordinate plane and then draw a line passing through the points.
After the line representing the linear equation form of the linear inequality is drawn, we select a point either side of the line to determine which side of the line is true for the given inequality and then shade the side that satisfies the inequality.
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Organized Videos:
✅Graph Linear Inequalities in Two Variables
• Graph Linear Inequalit...
✅Graph Linear Inequalities in Two Variables | Learn About
• Graph Linear Inequalit...
✅Graph Linear Inequalities | Slope Intercept Form
• Graph Linear Inequalit...
✅Graph Linear Inequalities | Standard Form
• Graph Linear Inequalit...
✅Graph Linear Inequalities | Horizontal and Vertical
• Graph Linear Inequalit...
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Spends 1 hour in algebra: makes no sense
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i was having a headache on these problems for hours, so happy to finally understand it in a matter of mins.

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[@brianmclogan]

You are
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This man has made an impact on so many students outside the classroom

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[@brianmclogan]

happy to be able to help!

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I spend hours in my algebra II class not understanding anything and feeling hella stupid but watch a 5min youtube video and learn the whole concept so easily. Thank you

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I’m taking the regents today, and this video really helped me a lot. Thanks! :)

[@brianmclogan]

you are very welcome!

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Me to

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[@brianmclogan]

you are very welcome!

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[@idonthavetime2think4fancyn99]

you did not flip the sign when you divide it by -5, i saw it before you erased...

[@brianmclogan]

yes that is because I was not actually solving an inequality but an equation.

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i’ve spent like three weeks on this. didn’t understand a thing.
i spend 4:49 minutes and i understand it almost perfectly

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Happy to help Edilberto

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THIS IS SO FREAKY UNDERSTANDABLE

[@jigyasa469]

In which standard is it taught there?
Like we r studying it in class 11 here In india
B/w it was just an awsome explaination❤️

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when i was in the U.S i learned it in 7th grade but even though i live somewhere else now we still have these on our highschool exams

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Brian carries me through Algebra.

[@sleepymoose7645]

I dont know is Flipped the sign...
Can you please what do you mean about that?

[@JCASEYPENDLETON]

What would I use as a test point if 0,0 is in my boundary line?

[@brianmclogan]

any point not on the boundry line say (1,1) or (-1,1) or (1,-1)

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You saved me, thank you.

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Thanks for helping me. This was way simpler than the books make it.

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Thanks for helping us

[@priscillaharrington2262]

Wasn't the graph supposed to be shaded above the line because it's greater than/equal, to that way it makes the bottom boundary lines true? The final equation is y >= 4/5X - 5, right?

[@hinezsantos392]

Yes, also, he did not change the inequality sign when he divided 25 into -5. So it is supposed to be shaded above the line

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learned this yesterday and forgot. And he just taught it the same way my teacher did! bravo! i love thanks so much ☺️!

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Sharren Henry me too

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Me too

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[@brianmclogan]

You are very welcome Nizami

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Thank you , keep it up , a very useful for a student like me 💕

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Thank you very much for this video. It is very easy now for me to understand.

[@derpmarc288]

what i do not understand is how do u know wich variable is positive and wich is negative

[@brianmclogan]

what do you mean?

[@SandoPlaysPRO]

You do -A/B. So it would be -4/-5 = 4/5, which is the slope he has in the board

[@imjusthere5935]

Thank you so much video was so clear and useful i was absent 1 day and teacher says u have to get notes from classmates and i woud feel akward to do that now im ready for my 2 tests this week thanks again so much im will always from now on check ur channel for stuff i don't understand

[@brianmclogan]

you are very welcome! happy to be able to help!

[@Dereck27]

Pretty sure if you divide by a negative number, the signs switch. I know you said it doesn’t matter but I’m just to memorize

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Thank you for that video it help my daughter thank you 😊😊😊

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You make math more easy for me

[@Bhaalg0rn]

it's one of those things that we, all mathematicians, do like grocers most of the time. Draw a line, check a point to be safe aaaaand done

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Your the man! thank you.

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nice to spend our times in YT for studies

[@aperson4253]

Thanks

[@brianmclogan]

you are very welcome!

[@RaeganHarris08]

Thank you so much! You saved me a ton!!❤

[@Chawnsey1234]

You are freaking amazing!

[@nikri8671]

How do u make a test point and where do you know to shade in the graph?

[@reeeeeeeoli6537]

test point is commonly (0,0). For the shaded area, replace the x and y in your inequality to the test point. If it comes out as true, the test point is IN the shaded area. If false, it is NOT in the shaded area.

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Thanks ☺️☺️☺️

[@cristhianmaradiaga1259]

This video helped me a lot

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how the heck. im in shock this makes so much sense omg

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Thank u sooooo much sir❤️

[@mahraalkhyeli3715]

wow...i thought inequalities are hard!

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Thank you

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Im in college finished calc first semester and forgot the rest of my math after that now I'm here junior year of college :)

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Thank u so much💛

[@elaine_2689]

Thank you soo much for the help sir :)

[@f32.5immunity9]

Real class:Ah man it was too fast I couldn’t get it
Real class but its a video:*Pauses every line*Ah I see its now easier.

[@almash.2625]

Thank you thank you!!!

[@AllyChuwi]

Thank you so much for this helpful guide, sir💙

[@rjjones8672]

So what if we have to graph 2 lines and shade 2 areas? Is it the same process?

[@emilylake9967]

THANK YOU!!!!!!!!!! finally it makes sense

[@meiandmyself5494]

Can you show us how to solve this linear inequality?
Y2..... if (-3,2)

[@yasminepadilla]

Okay , I won't worry about switching sign for linear inequalities when I am checking because I have been getting those wrong but hopefully not anymore!

[@francogalloso2167]

really clear your explanation. thanks

[@user-kd2en4tm9d]

How about those undivided numbers? Like 3x + 4y > 6?

[@brianmclogan]

they you would just have fractions

[@mrdoctorB055]

Hmmm it's helpful
Thanks

[@neha_suresh]

Thank you Brian!💙

[@tiad2739]

*watches the night before midterms(