Answer:
Equation of line is given by:
[tex]y=2x+14[/tex]
Step-by-step explanation:
Given points:
[tex](-8,-2)\ and\ (-4,6)[/tex]
Slope of line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is a point on the line
[tex]m=\frac{6-(-2)}{-4-(-8)}[/tex]
[tex]m=\frac{6+2}{-4+8}[/tex]
[tex]m=\frac{8}{4}[/tex]
∴ [tex]m=2[/tex]
Point-slope equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is slope of line.
Using point [tex](-8,-2)[/tex] and slope [tex]m=2[/tex] point-slope equation of line is given by:
[tex]y-(-2)=2(x-(-8))[/tex]
Simplifying.
[tex]y+2=2(x+8)[/tex]
Using distribution.
[tex]y+2=2x+16[/tex]
Subtracting 2 to both sides.
[tex]y+2-2=2x+16-2[/tex]
[tex]y=2x+14[/tex]
Thus, equation of line is [tex]y=2x+14[/tex]
