Question

How do you find the slope and y intercept of `3x +4y = 5`?

Answer 1

Slope: `-3/4`
`y`-intercept: `(0, 5/4)`

Explanation:

To find the slope of a standard equation, we need to make `y` by itself.

`3x + 4y = 5`

First, subtract `color(red)(3x)` from both sides of the equation:
`3x + 4y quadcolor(red)(-quad3x) = 5 quadcolor(red)(-quad3x)`

`4y = 5 - 3x`

Divide both sides by `color(red)4`:
`(4y)/color(red)4 = (5-3x)/color(red)4`

`y = 5/4 - (3x)/4`

The slope is the value multiplying the `x`, so the slope is `-3/4`.

`--------------------`

To find the `y`-intercept, we set `x` to be `0` and find the value of `y`:
`y = 5/4 - (3x)/4`

`y = 5/4 - (3(0))/4`

Simplify:
`y = 5/4 - 0`

`y = 5/4`

So the `y`-intercept is at `(0, 5/4)`.

Hope this helps!