Question

How do you find the slope of `5x + 3y = -2`?

Answer 1

slope `=-5/3`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b can be extracted 'easily'.

Rearrange 5x + 3y = - 2 into this form.

leave 5y on the left and move 5x to the right.

subtract 5x from both sides

`cancel(5x)+3y-cancel(5x)=-2-5xrArr3y=-2-5x`

now divide both sides by 3

`(cancel(3) y)/cancel(3)=-2/3-(5)/3 x`

`rArr"slope" =-5/3`