Skill: 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:

1. Substitute $x=0$ into the equation.
2. Solve for $y$.
3. 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.