The equation of a line in slope-intercept form is given as:
[tex]\begin{gathered} y=mx+c \\ ^{\prime}m^{\prime}\text{ is the slope} \\ ^{\prime}c^{\prime}\text{ is the intercept on y-axis} \end{gathered}[/tex]The slope,m, is calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} \text{For the points (-8,}-2)\text{ and (-4,6)} \\ x_1=-8,y_1=-2_{}_{}_{} \\ x_2=-4,y_2=6 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} m=\frac{6-(-2)}{-4-(-8)} \\ m=\frac{6+2}{-4+8} \\ m=\frac{8}{4} \\ m=2 \end{gathered}[/tex][tex]\begin{gathered} Equation\text{ of the line is:} \\ m=\frac{y-y_1}{x-x_1} \\ 2=\frac{y-(-2)}{x-(-8)} \\ 2=\frac{y+2}{x+8} \\ y+2=2(x+8) \\ y+2=2x+16 \\ y=2x+16-2 \\ y=2x+14 \end{gathered}[/tex]Hence, the equation of the line in slope-intercept form is:
y= 2x + 14
