Question

(0,-2) and (-5,3)
Slope =
y-intercept =
Slope intercept equation:

Answer 1

Slope =
`-1`

y-intercept =
`-2`

Slope-intercept equation:
`y=-1x-2`

Explanation:

Let
`m` equal slope.

Start with:

`m=(y_2-y_1)/(x_2-x_1)`

For Point (0,-2):

`x_1=0`,
`y_1=-2`

For Point (-5,3):

`x_2=-5`,
`y_2=3`

Let's substitute those values in.

`m=(3-(-2))/(-5-0)`

Rewrite.

`m=(3+2)/(-5-0)`

Combine like terms.

`m=(5)/(-5)`

Simplify.

`m=-1`

__

Let
`b` equal the y-intercept.

Since we have our slope, let's format an equation as:

`y=mx+b`

Substitute.

`y=-1x+b`

We can use either point for this next part, let's use point (-5,3).

Since the numbers are representatives of both
`x` &
`y`, we can substitute:

`3=-1(-5)+b`

Multiply.

`3=5+b`

Subtract
`5` from both sides of the equation.

`-2=b`

Let's rewrite.

`b=-2`

__

Now that we have both our slope & y-intercept, let's put this into slope-intercept form.

`y=mx+b`

Substitute.

`y=-1x-2`