Question

A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?

Answer 1

Answer:

$y=\frac{1}{3}x-8$

Step-by-step explanation:

Slope-intercept form of an equation is written as $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

The slope of a line that passes through the points $(x_1,\: y_1)$ and $(x_2, \: y_2)$ is $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$. Using the coordinates $(6,-6)$ and $(9,-5)$ as given in the problem, we have slope of this line to be:

$m=\frac{-5-(-6)}{9-6}=\frac{1}{3}$.

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

$-6=\frac{1}{3}(6)+b, \\ b=-8$

Therefore, the equation of this line in slope-intercept form is $\fbox{ y=\frac{1}{3}x-8 }$.