Question

A line has a slope of 10 and includes the points ( – 4,10) and ( – 6,a). What is the value of a? a=

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{a}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{a}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 10 }\implies \cfrac{a-10}{-6+4}=10\implies \cfrac{a-10}{-2}=10 \\\\\\ a-10=-20\implies \boxed{a=-10}`

Answer 2

Slope

Let's try and find the value of a.

Use our slope formula:

`\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}`

Substitute all the values.

`\sf{10=\cfrac{a-10}{-6-(-4)}}`

Simplify.

`\sf{10=\cfrac{a-10}{-6+4}}`

`\sf{10=\cfrac{a-10}{-2}}`

Multiply both sides by -2.

`\sf{-20=a-10}`

Add 10 to both sides:

`\sf{-20+10=a}`

Simplify.

`\sf{-10=a}`

Therefore, a = -10.