Respuesta :
The equation of a line in the slope-intercept form is y = mx + b.
Given the points (-4, -15) and (5, 12), follow the steps below to find the equation of the line.
Step 01: Substitute the first point in the equation.
Given the point (-4, -15)
Then, when x = -4, y = -15
[tex]\begin{gathered} y=mx+b \\ -15=m*(-4)+b \\ -15=-4m+b \end{gathered}[/tex]Add 4m to both sides to solve for b:
[tex]\begin{gathered} -15+4m=-4m+4m+b \\ b=-15+4m \end{gathered}[/tex]Step 02: Substitute b in the equation.
[tex]\begin{gathered} y=mx+(-15+4m) \\ y=mx-15+4m \end{gathered}[/tex]Step 03: Substitute the second point in the equation.
Given the point (5, 12).
Then, when x = 5, y = 12
Substituting it in the equation:
[tex]\begin{gathered} y=mx-15+4m \\ 12=m*5-15+4m \\ 12=5m-15+4m \\ 12=9m-15 \end{gathered}[/tex]Adding 15 to both sides and then dividing the sides by 9:
[tex]\begin{gathered} 12+15=9m-15+15 \\ 27=9m \\ \frac{27}{9}=\frac{9}{9}m \\ 3=m \\ m=3 \end{gathered}[/tex]Step 04: Find b and substitute b and m in the equation.
[tex]\begin{gathered} b=-15+4m \\ b=-15+4*3 \\ b=-15+12 \\ b=-3 \end{gathered}[/tex]
The equation of the line is:
[tex]y=3x-3[/tex]Answer:
[tex]y=3x-3[/tex]