Question

A line passes through the point (-6,3) and a slope of 5/2

Answer 1

Explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point on a line

We have

`(-6,\ 3)\to x_1=-6,\ y_1=3,\ m=(5)/(2)`

Substitute:

`y-3=(5)/(2)(x-(-6))\\\\y-3=(5)/(2)(x+6)`

Convert to the slope-intercept form

`y=mx+b`

m - slope

b - y-intercept

`y-3=(5)/(2)(x+6)` use the distributive property

`y-3=(5)/(2)x+(5)/(2\!\!\!\!\diagup_1)\cdot6\!\!\!\!\diagup^3`

`y-3=(5)/(2)x+15` add 3 to both sides

`y=(5)/(2)x+18`

Convert to the standard form:

`Ax+By=C`

`y=(5)/(2)x+18` multiply both sides by 2

`2y=5x+36` subtract 5x from both sides

`-5x+2y=36` change the signs

`5x-2y=-36`