Question

What is the equation in standard form of the line that passes through the points (3,5) and (-7,2)? (A.2B)

Answer 1

The standard form: Ax + By = C.

The point-slope form:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have the points (3, 5) and (-7, 2). Substitute:

`m=(2-5)/(-7-3)=(-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`

Answer: 3x - 10y = -41