Question

Complete the equation of the line through (2,1) and (5,-8)
Use exact numbers.
y=___x____

Answer 1

Answer: 7

Explanation:

Yes

Answer 2

Given two points
`(x_1,y_1)` and
`(x_2,y_2)`, the line passing through them is given by

`(x-x_2)/(x_1-x_2) = (y-y_2)/(y_1-y_2)`

In your case,
`(x_1,y_1)=(2,1)` and
`(x_2,y_2) = (5,-8)`

So, the equation of the line becomes

`(x-5)/(2-5) = (y+8)/(1+8) \iff (x-5)/(-3) = (y+8)/(9) \iff 9(x-5) = -3(y+8)`

If we expand both sides, we have

`9x-45 = -3y -24`

Add 24 to both sides:

`9x-21 = -3y`

Divide both sides by -3:

`y=-3x+7`