The point-slope form:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, -4) and (5, 1). Substitute:
[tex]m=\dfrac{1-(-4)}{5-3}=\dfrac{5}{2}\\\\y-(-4)=\dfrac{5}{2}(x-3)[/tex]
The standard form: [tex]Ax+By=C[/tex]
[tex]y+4=\dfrac{5}{2}(x-3)[/tex] multiply both sides by 2
[tex]2y+8=5(x+3)[/tex] use distributive property
[tex]2y+8=5x+15[/tex] subtract 2y from both sides
[tex]8=5x-2y+15[/tex] subtract 15 from both sides
[tex]-7=5x-2y[/tex]
Answer: 5x - 2y = -7
