Respuesta :
The equation of a line in the slope-intercept form is y = mx + b, where "m" is the slope and b is the y-intercept.
To find the equation of the line given two points (x, y), follow the steps below.
Step 01: Substitute the point (-3, 2) in the equation.
To do it, substitute x by -3 and y by 2.
[tex]\begin{gathered} 2=m\cdot(-3)+b \\ 2=-3m+b \end{gathered}[/tex]Isolate b by adding 3m to both sides of the equation.
[tex]\begin{gathered} 2+3m=-3m+b-3m \\ 2+3m=-3m+3m+b \\ 2+3m=b \end{gathered}[/tex]Step 02: Substitute b in the equation of the line.
Knowing that b = 2 + 3m. Then,
[tex]\begin{gathered} y=mx+b \\ y=mx+2+3m \end{gathered}[/tex]Step 03: Substitute the point (-6, -2) in the equation from step 02.
To do it, substitute x by -6 and y by -2.
[tex]\begin{gathered} -2=m\cdot(-6)+2+3m \\ -2=-6m+2+3m \\ -2=-3m+2 \end{gathered}[/tex]Isolate "m" by subtracting 2 from both sides.
[tex]\begin{gathered} -2-2=-3m+2-2 \\ -4=-3m \end{gathered}[/tex]Finally, divide both sides by -3:
[tex]\begin{gathered} \frac{-4}{-3}=\frac{-3}{-3}m \\ \frac{4}{3}=m \end{gathered}[/tex]Knowing "m", use the equation from step 1 to find "b".
Step 04: Find "b".
[tex]\begin{gathered} b=2+3m \\ \end{gathered}[/tex]Substituting m by 4/3 and solving the equation:
[tex]\begin{gathered} b=2+3\cdot\frac{4}{3} \\ b=2+\frac{3\cdot4}{3} \\ b=2+4 \\ b=6 \end{gathered}[/tex]Answer: The equation of the line is:
[tex]y=\frac{4}{3}x+6[/tex]