Skill: Determine the y-intercept from a graph

The $y$-intercept is where a graph crosses the $y$-axis. Since every point on the $y$-axis has an $x$-coordinate of $0$, the $y$-intercept always has the form

$$(0,b).$$

The value $b$ is also the constant term in the equation

$$y=mx+b.$$

Example: A line crosses the $y$-axis at the horizontal grid line labeled $4$. It crosses the $x$-axis at $8$.

1. Find the $y$-axis. It is the vertical axis.

2. Find where the line crosses that axis.

3. Read the $y$-value using the scale. The line crosses at $(y=4)$.

4. Write the intercept as an ordered pair:

$$(0,4)$$

Therefore, the $y$-intercept is $((0,4))$. This means that when the input $(x=0)$, the output is $(y=4)$. In an equation such as

$$y=-\frac{1}{2}x+4,$$

the $4$ is the constant term $b$.

Do not use the point $((8,0))$, because that is where the graph crosses the $x$-axis, not the $y$-axis.