Determine the y-intercept from an equation

The y-intercept is the y-coordinate of the point where a linear relation crosses the y-axis, found by setting $x=0$ and solving for $y$ ; in $y=mx+b$ , it is $b$ , and in other forms it may require rearranging the equation. This connects an equation to its graph and distinguishes the y-intercept from the x-intercept; nonlinear relations, vertical lines, and generalized parameter-based cases are not included.

Detailed Explanation: Determine the y-intercept from an equation

The y-intercept is where a line crosses the $y$ -axis. Every point on the $y$ -axis has an $x$ -coordinate of $0$ .

To find the y-intercept:

Substitute $x=0$ into the equation.
Solve for $y$ .
Write the intercept as the point $(0,y)$ .

Example

Find the y-intercept of

2x+3y=12

Set $x=0$ :

2(0)+3y=12

Simplify:

3y=12

Divide both sides by $3$ :

y=4

Therefore, the y-intercept is

\boxed{(0,4)}

The line crosses the $y$ -axis at $(0,4)$ . The y-intercept is not found by setting $y=0$ ; that would find the x-intercept instead.

Learn by doing: Determine the y-intercept from an equation

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Linear Equations - Find Y Intercept (Integer) - Standard Form

Earned ?