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Find the X and Y Intercepts of a Line Using Algebra
> ... Math > Slopes, Intercepts, Equation of a Straight Line > Find the X and Y Intercepts of a Line Using Algebra

When the equation is written in the slope-intercept form (y=mx+b), we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept, we set y = 0 and solve the equation for x. This is because when y = 0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

Find the X and Y-Intercepts of a Line Using Algebra

Video Source (08:37 mins) | Transcript

To find y-intercept, set x = 0 and solve for y. The point will be (0, y).

To find x-intercept, set y = 0 and solve for x. The point will be (x, 0).

Additional Resources

Practice Problems

1. Find the y-intercept of the line: (
Solution
x
Solution:
\(y=-9\)
)
\({\text{y}}=-3{\text{x}}-9\)2. Find the x-intercept of the line: (
Solution
x
Solution:
\(x=3\)
)
\({\text{y}}=-4{\text{x}}+12\)3. Find the y-intercept of the line: (
Solution
x
Solution:
\(y=9\)
Details:
Written solution: To find y-intercept: set \({\color{Red}x = 0}\) and solve for y. The point will be (0,y):

\(y − 9 = 3{\color{Red}x}\)

Substitute \({\color{Red}0}\) in for \({\color{Red}x}\):

\(y − 9 = 3 {\color{Red}(0)}\)

Multiply 3 times 0, which gives us:

\(y − 9 = {\color{Red}0}\)

Then add 9 to both sides to isolate y:

\(y − 9 {\color{Red}+9} = 0 {\color{Red}+9}\)

Which gives us:

\(y = 9\)

So the y-intercept is \((0,9)\).
)
\({\text{y}} − 9 = 3x\)4. Find the x-intercept of the line: (
Solution
x
Solution:
\(x=6\)
)
\({\text{y}} + 12 = 2x\)5. Find the y-intercept of the line: (
Solution
x
Solution:
\(y=-4\)
)
\({\text{x}}+6{\text{y}}=-24\)6. Find the x-intercept of the line: (
Solution
x
Solution:
\(x=-4\)
Details:
To find x-intercept: set \({\color{Red}y = 0}\) and solve for x. The point will be (x,0):

\(5{\text{x}}+4{\text{y}}=-20\)

Substitute \({\color{Red}0}\) in for y:

\(5{\text{x}}+4{\color{Red}(0)}=-20\)

Multiply 4 times 0 which gives us:

\(5{\text{x}}+{\color{Red}0}=-20\)

Add 5x to 0:

\(\frac{1}{5}(5{\text{x}})\) = \(5{\text{x}}=-20\)

Then multiply both sides by \(\dfrac{1}{5}\) (or divide both sides by 5, both will give you the same solution):

\(-20\dfrac{1}{5}\)

Which gives us:

\({\text{x}}=-4\)

So they x-intercept is \(-4,0)\)
)
\(5{\text{x}}+4{\text{y}}=-20\)

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