Question

write an equation of a line that passes through the following tow points (4, -6) and (2, 8) show work

Answer 1

`y = -7x + 22`

Explanation:

Given

`(x_1,y_1) = (4,-6)`

`(x_2,y_2) = (2,8)`

Required

Determine the line equation

This question will be answered using linear interpolation.

This is represented as thus:

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

Substitute values for x1,x2,y1 and y2

`(y - (-6))/(x - 4) = (8 - (-6))/(2 - 4)`

`(y +6)/(x - 4) = (8 +6)/(2 - 4)`

`(y +6)/(x - 4) = (14)/(-2)`

`(y +6)/(x - 4) =-7`

Cross Multiply

`y + 6 = -7(x - 4)`

`y + 6 = -7x + 28`

Make y the subject

`y = -7x + 28-6`

`y = -7x + 22`