Question

How do you find the slope and intercept of `2x+3y=6`?

Answer 1

Slope: `-2/3`
x-intercept: `(3, 0)`
y-intercept: `(0, 2)`

Explanation:

`2x + 3y = 6`

To find the slope, first make the equation into slope-intercept form:

Subtract `color(blue)(2x)` from both sides of the equation:
`2x + 3y quadcolor(blue)(-quad2x) = 6 quadcolor(blue)(-quad2x)`

`3y = 6 - 2x`

Divide both sides by `color(blue)3`:
`(3y)/color(blue)3 = (6-2x)/color(blue)3`

`y = 2 - 2/3x`

We know that the slope is the value multiplied by `x`, meaning that the slope is `-2/3`.

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

To find the x-intercept, plug in `0` for `y` and solve for `x`:
`0 = 2 - 2/3x`

Simplify:
`-2 = -2/3x`

`3 = x`

So the `x`-intercept is at `(3, 0)`.

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

To find the y-intercept, plug in `0` for `x` and solve for `y`:
`y = 2 - 2/3(0)`

`y = 2 - 0`

`y = 2`

So the `y`-intercept is at `(0, 2)`.

Hope this helps!

Answer 2

See below:

Explanation:

We can find the `x`-intercept by setting `y` equal to zero. We get

`2x=6=>x=3`

This is our `x`-intercept.

Similarly, we can set `x` equal to zero to find the `y`-intercept. We get

`3y=6=>y=2`

This is our `y`-intercept.

Next, we can convert this equation into slope-intercept form

`y=mx+b`, with slope `m`

We can start by subtracting `2x` from both sides to get

`3y=-2x+6`

Next, divide both sides by `3` to get

`y=-2/3x+2`

We see that our slope, the coefficient on `x` is `-2/3`.

Hope this helps!