In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
point 01 (-3 , 4)
point 02 (5 , 2)
Step 02:
equation of the line:
slope:
[tex]m\text{ =}\frac{y2-y1}{x2-x1}=\frac{2-4}{5-(-3)}=\frac{-2}{5+3}=\frac{-2}{8}=\frac{-1}{4}[/tex]Point-slope form of the line:
(y - y1) = m (x - x1)
(y - 4) = -1 / 4 (x - (-3))
(y - 4) = -1 /4 (x + 3)
[tex]\begin{gathered} y\text{ - 4 =}\frac{-1}{4}x-\frac{3}{4} \\ \\ y\text{ = }\frac{-1}{4}x\text{ -}\frac{3}{4}+4 \\ \\ y\text{ = }\frac{-1}{4}x+\frac{13}{4} \end{gathered}[/tex]The answer is:
[tex]y=\frac{-1}{4}x+\frac{13}{4}[/tex]