Given the question:
Point (x,y) = -6,1
Slope (m) = -3/2
Let's use the Slope-Intercept Formula in making the equation of the line.
[tex]\text{ y = mx + b}[/tex]Step 1: Substituting m = -3/2 and x,y = -6,1 in y = mx + b, let's determine the value of the y-intercept (b).
[tex]\text{ y = mx + b }\rightarrow\text{ 1 = (-}\frac{3}{2})(-6)\text{ + b}[/tex][tex]\text{ 1 = }\frac{18}{2}\text{ + b }\rightarrow\text{ 1 = 9 + b}[/tex][tex]1\text{ - 9 = 9 + b - 9}[/tex][tex]-8\text{ = b ; b = -8}[/tex]Step 2: Let's now complete the equation by substituting m = -3/2 and b = -8 in the formula.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-}\frac{3}{2})x\text{ + (-8)}[/tex][tex]\text{ y = -}\frac{3}{2}x\text{ - }8[/tex]Therefore, the equation of the line is y = (-3/2)x - 8.
