ANSWER
[tex]\begin{gathered} m=-\frac{3}{2} \\ c=2 \end{gathered}[/tex]
EXPLANATION
Given;
[tex]3x+2y=8[/tex]
Re-write the equation in the standard form;
[tex]\begin{gathered} y=mx+c \\ 3x+2y=8 \\ 2y=-3x+8 \end{gathered}[/tex]
solve for y by dividing both sides by 2;
[tex]\begin{gathered} 2y=-3x+8 \\ \frac{2y}{2}=-\frac{3x}{2}+\frac{8}{2} \\ y=-\frac{3}{2}x+4 \\ m=-\frac{3}{2} \end{gathered}[/tex]
The line parallel to this line must have the same slope. Hence, the equation of the line that passes through points (-2,5) is;
[tex]\begin{gathered} m=-\frac{3}{2} \\ y=5 \\ y=mx+c \end{gathered}[/tex]
Substitute the value of point y and the slope;
[tex]\begin{gathered} y=mx+c \\ y=5 \\ 5=-\frac{3}{2}(-2)+c \\ 5=3+c \\ c=5-3 \\ =2 \\ y=-\frac{3}{2}x+2 \end{gathered}[/tex]
