Question

Find the equation of a line that goes through points (8,-9) and (-4,15)

Answer 1

Answer: y=-2x+7

Explanation:

The equation of a line

`\displaystyle\\\boxed {(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1) }`

(8,-9) (-4,15)

x₁=8 x₂=-4 y₁=-9 y₂=15

`\displaystyle\\(x-8)/(-4-8) =(y-(-9))/(15-(-9)) \\\\(x-8)/(-12)=(y+9)/(15+9) \\\\(x-8)/(-12)=(y+9)/(24)`

Let's multiply both parts of the equation by 24:

`\displaystyle\\(24(x-8))/(-12) =y+9\\\\-2(x-8) =y+9\\\\-2x+16=y+9 \\\\-2x+16-9=y+9-9\\\\-2x+7=y\\\\Thus,\\\\y=-2x+7`