Question

How do you find the slope of 8x - 3y = -5?

Answer 1

The slope of `8x-3y=-5` is `8/3`

Explanation:

Method 1
For a linear equation in standard form
`color(white)("XXXX")` `Ax+By=C`
the slope is given by the equation
`color(white)("XXXX")` `m=-A/B`

In this case that becomes
`color(white)("XXXX")` `m= - 8/(-3) = 8/3`

Method 2 (more common, but more work)
Convert the equation into "slope-point form":
`color(white)("XXXX")` `y = mx+b`
`color(white)("XXXX")` `color(white)("XXXX")`with a slope of `m` and a y-intercept of `b`

`8x-3y = -5`

`rarr` `color(white)("XXXX")` `-3y = -8x -5`

`rarr` `color(white)("XXXX")` `y = 8/3x +5/3`