Question

Find the equation, in standard form, of the line passing through the points (5,1) and (-2,3)

Answer 1

The standard form:

`Ax+By=C`

The point-slope form:

`y-y_1=m(x-x_1)`

m - slope

(x₁, y₁) - point

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (5, 1) and (-2, 3). Substitute:

`m=(3-1)/(-2-5)=(2)/(-7)=-(2)/(7)`

`y-1=-(2)/(7)(x-5)` use distributive property

`y-1=-(2)/(7)x+(10)/(7)` multiply both sides by 7

`7y-7=-2x+10` add 7 to both sides

`7y=-2x+17` add 2x to both sides

`\boxed{2x+7y=17}`