Question

(-5, 7) with a slope of 5/3 write in standard form.

Answer 1

`\large\boxed{5x-3y=-46}`

Explanation:

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

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

We have

`(-5,\ 7)\to x_1=-5,\ y_1=7\\\\m=(5)/(3)`

Substitute:

`y-7=(5)/(3)(x-(-5))\\\\y-7=(5)/(3)(x+5)`

The standard form of an equation of a line:

`Ax+By=C`

Convert

`y-7=(5)/(3)(x+5)\qquad\text{multiply both sides by 3}\\\\3y-21=5(x+5)\qquad\text{use distributive property}\\\\3y-21=5x+25\qquad\text{subtract 25 from both sides}\\\\3y-46=5x\qquad\text{subtract 3y from both sides}\\\\-46=5x-3y\to5x-3y=-46`