Question

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

Answer 1

Answer:

$y = -7x + 22$

Step-by-step 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:

$\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute values for x1,x2,y1 and y2

$\frac{y - (-6)}{x - 4} = \frac{8 - (-6)}{2 - 4}$

$\frac{y +6}{x - 4} = \frac{8 +6}{2 - 4}$

$\frac{y +6}{x - 4} = \frac{14}{-2}$

$\frac{y +6}{x - 4} =-7$

Cross Multiply

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

$y + 6 = -7x + 28$

Make y the subject

$y = -7x + 28-6$

$y = -7x + 22$