Question

A line has a slope of

-5 and includes the points (7,p) and (8,4). What is the value of p?

Answer 1

Answer p= 9

Step by step

Slope is -5/1 as y/x

Slope can be found with slope formula

y2 - y1 over x2 - x1

We only need to solve for y since “p” is a y value

Y2 - y1 = -5
4 - p = -5
Subtract 4 from both sides to isolate p
4 - 4 - p = -5 -4
-p = -9
p = 9

So now we have ( 7, 9) and ( 8, 4)

y2 - y1 over x2 - x1

4 - 9 over 8 - 7 = -5/1 slope

Problem solved!

Answer 2

`(\stackrel{x_1}{7}~,~\stackrel{y_1}{p})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{p}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{7}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -5 }\implies \cfrac{4-p}{1}=-5 \\\\\\ 4-p=-5\implies 4=-5+p\implies 9=p`