We have to find the equation of the line that passes through points (2,-5) and (7,3).
We can start by calculating the slope m as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{7-2}=\frac{3+5}{5}=\frac{8}{5}[/tex]With one point and the slope, we can write the line equation in slope-point form and then rearrange it:
[tex]\begin{gathered} y-y_2=m(x-x_2) \\ y-3=\frac{8}{5}(x-7) \\ y-3=\frac{8}{5}x-\frac{56}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+3\cdot\frac{5}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+\frac{15}{5} \\ 5y=8x-56+15 \\ 5y=8x-41 \\ -8x+5y+41=0 \\ 8x-5y-41=0 \end{gathered}[/tex]The equation in general form is 8x-5y-41 = 0.
We can sketch it as:
