How to Graph Linear Equations Using the Intercepts Method

Co-authored by Taylor Klein

Last Updated: January 18, 2024 Fact Checked

There are many ways to graph a line: plugging in points, calculating the slope and y-intercept of a line, using a graphing calculator, etc. This article will teach you how to graph a line using intercepts.

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Identify both. For the sake of clarity, let the independent be x and the dependent be y. ^{[1]
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This will generate a coordinate for your y-intercept. First, substitute x to zero. Then, subtract the product from both sides of the equation. Note that the operation you will perform with both sides depends on the sign of your number. In this case the number is zero so we will use its opposite, subtraction. After that, divide three from both sides. And, VOILA! You have the answer. ^{[3]
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(x,y) Since x=0, your coordinate pair will be similar to: (0,y).
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Again, since you set y=0, your coordinate pair will look something like: (x,0).
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Question

Do we need to figure an equation out before knowing to change the x or y to 0, or can I change either/or in any equation?

Elena Himmerich

Community Answer

You do need an equation to figure out an x- or y-intercept, but it doesn't need to be in any specific form. For example, you could just as easily change a variable to zero in a standard form equation as you could in a point-slope form equation.

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What if there is something attached to the equation? (E.g. y/2 = 10-4x)

Technist

Community Answer

You can convert that into a linear equation like the one shown in the article. y/2 is the same as (1/2)y, so the coefficient is 1/2. You can also add 4x to both sides so that the equation is now 4x + (1/2)y = 10 and use the method shown in the article. By substituting 0 into x and then y, we get the intercepts (0, 20) and (5/2, 0). (Note: 5/2 = 2.5 so it doesn't matter which one you end up with.) You can then plot those two points and draw a straight line through both.

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Can we take other values of x and y in table?

Donagan

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Yes. A straight line is defined by two points. So if you're simply trying to graph a straight line, you can use any two pairs of coordinates (from the table) to find two points on the line. If, however, you want to use the intercepts method shown above, you would need to set either x or y equal to zero as shown in the article.

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Do this in pencil. You might make a mistake.

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X will always be the independent variable on the horizontal x-axis.

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Usually, you are dealing with an xy-coordinate plane.

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Warnings

In a coordinate pair, x always comes first. ^{[6]
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Always put parentheses around a coordinate pair, or you will convey the wrong mathematical message to a reader. ^{[7]
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