Question

What is the slope of the line that passes through the points (-4, -10)) and (-7, -19)

? Write your answer in simplest form.

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}`

Answer 2

Slope = 3

Explanation:

(-4, -10) and (-7, -19)

(x₁, y₁) (x₂, y₂)

y₂ - y₁ -19 - (-10) -19 + 10 -9

m = ------------ = ---------------- = ------------- = -------- = 3

x₂ - x₁ -7 - (-4) -7 + 4 -3

I hope this helps!