The Algebra of Lines:

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.

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

Khan Academy: Introduction to Intercepts (06:32 mins, Transcript)
Khan Academy: X-intercept of a Line (01:42 mins, Transcript)
Khan Academy: Intercepts from an Equation (04:07 mins, Transcript)

Practice Problems

Find the y-intercept of the line:
\({\text{y}}=-3{\text{x}}-9\)

Find the x-intercept of the line:
\({\text{y}}=-4{\text{x}}+12\)

Find the y-intercept of the line:
y − 9 = 3x

Find the x-intercept of the line:
y + 12 = 2x

Find the y-intercept of the line:
\({\text{x}}+6{\text{y}}=-24\)

Find the x-intercept of the line:
\(5{\text{x}}+4{\text{y}}=-20\)

Solutions

\({\text{y}}=-9\)
x = 3
y = 9 (Written Solution)

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

y − 9 = 3x

Substitute 0 in for x:

y − 9 = 3 (0)

Multiply 3 times 0, which gives us:

y − 9 = 0

Then add 9 to both sides to isolate y:

y − 9 + 9 = 0 + 9

Which gives us:

y = 9

So the y-intercept is (0,9)
x = 6
\({\text{y}}=-4\)
\({\text{x}}=-4\)(Written Solution)

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

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

Substitute 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:

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

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

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

Which gives us:

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

So they x-intercept is \((-4,0)\)