Let's begin by listing out the information given to us:
(x, y) = (3, 5), (-2, 6)
The general equation of a straight line function is given as:
[tex]\begin{gathered} y=mx+b \\ where\colon m=slope,b=y-intercept \end{gathered}[/tex]
We calculate the slope using:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{-2-3}=-\frac{1}{5} \\ m=-\frac{1}{5} \end{gathered}[/tex]
Substitute the slope into the, we have:
[tex]y=-\frac{1}{5}x+b[/tex]
We will proceed to for b, we have:
[tex]\begin{gathered} y=mx+b \\ m=-\frac{1}{5},(x,y)=(3,5) \\ 5=-\frac{1}{5}(3)+b\Rightarrow5=-\frac{3}{5}+b \\ 5=-\frac{3}{5}+b\Rightarrow b=5+\frac{3}{5} \\ b=\frac{28}{5} \\ y-y_1=m(x-x_1) \\ y-5=-\frac{1}{5}(x-3)\Rightarrow y-5=-\frac{1}{5}x+\frac{3}{5} \\ y-5=-\frac{1}{5}x+\frac{3}{5}(point-slopeform) \\ \end{gathered}[/tex]
