A graph has the points (0, 6) and (9, 0). Find the y-intercept.

Answer 1

The y-intercept of a linear equation is the point where the line crosses the y-axis. This occurs when $x=0$.

You already have one point on the line at the y-intercept, which is $(0,6)$. Therefore, the y-intercept is $6$.

To confirm this using the two points you have, you can find the equation of the line that passes through the points $(0,6)$ and $(9,0)$.

1. Calculate the slope (m):

$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-6}{9-0}=\frac{-6}{9}=-\frac{2}{3}$$

2. Use the slope-intercept form of the line:

The slope-intercept form is given by:

$$y=mx+b$$

where $m$ is the slope and $b$ is the y-intercept.

Using the slope $m=-\frac{2}{3}$ and the point $(0,6)$, we can substitute $(0,6)$ into the equation:

$$6=-\frac{2}{3}(0)+b$$

This simplifies to:

$$6=b$$

Thus, the y-intercept $b$ is indeed $6$.

So, the y-intercept is:

$$\boxed{{\displaystyle 6}}$$