Question

Complete the equation of the line through (-8, -2) and (-4, 6)

Answer 1

Answer:

Equation of line is given by:

$y=2x+14$  

Step-by-step explanation:

Given points:

$(-8,-2)\ and\ (-4,6)$

Slope of line $m=\frac{y_2-y_1}{x_2-x_1}$

where $(x_1,y_1)$ and $(x_2,y_2)$  is a point on the line

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

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

$m=\frac{8}{4}$

∴ $m=2$

Point-slope equation of line is given by:

$y-y_1=m(x-x_1)$  

where $(x_1,y_1)$ is a point on the line and $m$ is slope of line.

Using point $(-8,-2)$ and slope $m=2$ point-slope equation of line is given by:

$y-(-2)=2(x-(-8))$  

Simplifying.

$y+2=2(x+8)$  

Using distribution.

$y+2=2x+16$  

Subtracting 2 to both sides.

$y+2-2=2x+16-2$  

$y=2x+14$  

Thus, equation of line is $y=2x+14$