The equation of the line that has a slope m is
[tex]y=mx+b.[/tex]
Since [tex]m=\dfrac{3}{2},[/tex] the equation is
[tex]y=\dfrac{3}{2}x+b.[/tex]
This line passes through the point (4,-2), then the coordinates of this point satisfy the equation:
[tex]-2=\dfra{3}{2}\cdot 4+b,\\ \\-2=6+b,\\ \\b=-8.[/tex]
Answer: [tex]y=\dfrac{3}{2}x-8.[/tex]
