Question

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

Answer 1

`m=2/5`

Explanation:

Given the equation of a line, all we need to do is rearrange it into terms of `y=mx+b`

`5y-2x=-3`
`5y=2x-3` Add -2x to both sides to get `y` by itself
`y=2/5x-3/5` Divide all terms by 5

Now that the equation is in terms of slope-intercept, with the slope being `m` in `y=mx+b`, you can find the slope.

Answer 2

See a solution process below:

Explanation:

We can multiply each side of the equation by `color(red)(-1)` to put the equation in Standard Linear Form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

`color(red)(-1)(5y - 2x) = color(red)(-1) * -3`

`(color(red)(-1) xx 5y) - (color(red)(-1) xx 2x) = 3`

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

`-5y + 2x = 3`

`color(red)(2)x + color(blue)(-5)y = color(green)(3)`

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Substituting gives:

`m = (-color(red)(2))/color(blue)(-5) = 2/5`

Answer 3

slope=`2/5`

Explanation:

So you're going to want to get it into `mx+b=y` form, where `m` is the slope and `b` is the `x` intercept.

To rearrange the equation:
`5y-2x=-3`
add `2x` to each side, which cancels out `-2x` from the left side
`5y=-3+2x`
now divide each side by `5`, which crosses out the `5` in `5y`
`y=(-3+2x)/5`

You now have the correct arrangement of the equation and can even flip `-3` and `2x` to match the form of the equation you want it in

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

Now since you have the equation being divided by `5`, you have to divide both `2` and `3` by `5`, making your new equation:
`y=(2/5)x-(3/5)`

and following the equation we can now see that `m`, which is the slope, is equal to `2/5`.