The standard form: Ax + By = C.
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, 5) and (-7, 2). Substitute:
[tex]m=\dfrac{2-5}{-7-3}=\dfrac{-3}{-10}=0.3\\\\y-5=0.3(x-3)\qquad|\text{use distributive property}\\\\y-5=0.3x-0.9\qquad|\text{multiply both sides by 10}\\\\10y-50=3x-9\qquad|\text{add 50 to both sides}\\\\10y=3x+41\qquad|\text{subtract 3x from both sides}\\\\-3x+10y=41\qquad|\text{change the signs}\\\\3x-10y=-41[/tex]
Answer: 3x - 10y = -41
