Standard form: find x- and y-intercepts

key notes:

Standard Form of a Linear Equation

A linear equation in standard form is written as:

Ax+By=C

where A, B, and C are numbers, and x, y are variables.

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What are Intercepts?

• x-intercept: The point where the line crosses the x-axis.
  At this point, y=0
• y-intercept: The point where the line crosses the y-axis.
  At this point, x=0

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How to Find the Intercepts from Standard Form

To find the x-intercept:

• Put y=0 in the equation Ax+By=C
• Solve for x.

To find the y-intercept:

• Put x=0 in the equation Ax+By=C.
• Solve for y.

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Worked Examples

Example 1

Find x- and y-intercepts of:

2x+3y=12

• Find x-intercept: Set y=0

2x+3(0)=12  ⟹  2x=12  ⟹  x=6

So, x-intercept is (6,0)

• Find y-intercept: Set x=0

2(0)+3y=12  ⟹  3y=12  ⟹  y=4

So, y-intercept is (0,4).

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Example 2

Find x- and y-intercepts of:

4x−5y=20

• x-intercept: Put y=0

4x=20  ⟹  x=5

• y-intercept: Put x=0

−5y=20  ⟹  y=−4

Intercepts are (5,0)and (0,−4).

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Summary

Intercept	How to find	Set variable to
x-intercept	Solve Ax+By=C for x	y=0
y-intercept	Solve Ax+By=C for y	x=0

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Practice Questions

Find the x- and y-intercepts of:

1. 3x+4y=12

2. 5x−2y=10

3. x+y=7

4. 6x+3y=18

Learn with an example

Let’s Practice!