Answer :
We have the two points: (3, -12) and (13,8)
To find the equation:
Step 1. Label the coordinates as follows:
[tex]\begin{gathered} x_1=3 \\ y_1=-12 \\ x_2=13 \\ y_2=8 \end{gathered}[/tex]Step 2. Find the slope of the line with the slope formula:
[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]Substituting the values:
[tex]m=\frac{8-(-12)}{13-3}[/tex]simplifying the result:
[tex]\begin{gathered} m=\frac{8+12}{10} \\ m=\frac{20}{10} \\ m=2 \end{gathered}[/tex]Step 3. Use point (x1,y1) which is (3,-12) and the slope m=2 in the point slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values:
[tex]y-(-12)=2(x-3)[/tex]And we simplify to solve for y, also, we use distributive property on the right side to multiply 2 by x and 2 by -3:
[tex]y+12=2x-6[/tex]Finally, we substract 12 to both sides:
[tex]\begin{gathered} y+12-12=2x-6-12 \\ y=2x-18 \end{gathered}[/tex]Answer: y=2x-18
