Question

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, 3).

Answer 1

Answer:

$y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)$

OR

$y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)$

Step-by-step explanation:

Hi there!

Point-slope form: $y-y_1=m(x-x_1)$ where $m$ is the slope and $(x_1,y_1)$ is a point that falls on the line

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-4, 7) and (5, 3):

$m=\frac{\displaystyle 3-7}{\displaystyle 5-(-4)}\\\\m=\frac{\displaystyle 3-7}{\displaystyle 5+4}\\\\m=\frac{\displaystyle -4}{\displaystyle 9}$

Therefore, the slope of the line is $-\frac{\displaystyle 4}{\displaystyle 9}$. Plug this into $y-y_1=m(x-x_1)$ as $m$:

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

2) Plug a point into $y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

Because we're given two points, there are two ways we can write this equation:

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x-(-4))\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)$

OR

$y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)$

I hope this helps!