The standard form:
[tex]Ax+By=C[/tex]
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (5, 1) and (-2, 3). Substitute:
[tex]m=\dfrac{3-1}{-2-5}=\dfrac{2}{-7}=-\dfrac{2}{7}[/tex]
[tex]y-1=-\dfrac{2}{7}(x-5)[/tex] use distributive property
[tex]y-1=-\dfrac{2}{7}x+\dfrac{10}{7}[/tex] multiply both sides by 7
[tex]7y-7=-2x+10[/tex] add 7 to both sides
[tex]7y=-2x+17[/tex] add 2x to both sides
[tex]\boxed{2x+7y=17}[/tex]
