The form of the equation of a line is
y = m x + b
m is the slope
b is the y-intercept
Since the slope of the line is -3/2
[tex]m=-\frac{3}{2}[/tex]Substitute it in the form of the equation
[tex]y=-\frac{3}{2}x+b[/tex]To find b substitute x and y in the equation by the coordinates of a point on the line
Since the line passes through the point (4, -7), then
x = 4 and y = -7
[tex]\begin{gathered} -7=-\frac{3}{2}(4)\text{ + b} \\ -7=-6+b \end{gathered}[/tex]Add 6 to both sides to find b
-7 + 6 = -6 + 6 + b
-1 = b
Substitute the value of b in the equation
[tex]\begin{gathered} y=-\frac{3}{2}x+(-1) \\ y=-\frac{3}{2}x-1 \end{gathered}[/tex]The equation of the line is y = -3/2 x - 1
