### Home > AC > Chapter 7 > Lesson 7.3.1 > Problem7-85

7-85.

The point $\left(21, 32\right)$ is on a line with slope $1.5$.

1. Find the equation of the line.

The equation of a line is in the $y = mx + b$ format, where $m = \text{slope (growth)}$ and $b = y\text{-intercept (starting point)}$.

Substitute the slope and the $\left(x, y\right)$ point given in the problem into $y = mx + b$.

$y = mx + b\\y = 1.5x + b\\32 = \left(1.5\right)\left(21\right) + b$

Solve for $b$.

$b = 0.5\\ y = 1.5x + 0.5$

Don't forget to check your solution!

2. Find the coordinates of a third point on the line.

One way to find this is to substitute an $x$ or $y$ value of your choice into the equation you found in part (a).

Sam substitutes the value $x = 4$ into the equation.
$y = 1.5 \left(4\right) + 0.5\\y = 6.5$
The coordinates of the third point that Sam found are $\left(4, 6.5\right)$.

Complete the table in the eTool below to find the equation of the line and additional points.
Click the link at right for the full version of the eTool: AC 7-85 HW eTool