Question

What is the equation in slope intercept form that passes through the point (3,9) and has a slope of -5?

Answer 1

`y=-5x+24`

Explanation:

Given:

Point: `(3,9)`

Slope: `-5`

First determine the point-slope form , then solve for `y` to get the slope-intercept form.

Point-slope form:

`y-y_1=m(x-x_1)`,

where:

`m` is the slope, and `(x_1,y_1)` is a point on the line.

Plug in the known values.

`y-9=-5(x-3)` `larr` Point-slope form

Slope-intercept form:

`y=mx+b`,

where:

`m` is the slope and `b` is the `y`-intercept.

Solve for `y`.

Expand the right-hand side.

`y-9=-5x+15`

Add `9` to both sides.

`y=-5x+15+9`

Simplify.

`y=-5x+24` `larr` Slope-intercept form

Answer 2

Since the slope-intercept form is `y = mx + b` and we do not know the `y`-intercept (`b`), substitute what is known (the slope and the point's coordinates), solve for `b`, then obtain `y = -5x + 24`.

Explanation:

The slope-intercept form is `y = mx + b`. First, we write down what we already know:
The slope is `m = -5`,
And there's a point `(3, 9)`.

What we do not know is the `y`-intercept, `b`.
Since every point on the line must obey the equation, we could substitute the `x` and `y` values that we already have:
`y = mx + b` becomes `9 = (-5) * 3 + b`

And then solve algebraically:
`9 = (-5) * 3 + b`
Multiply:
`9 = (-15) + b`
Add both sides by `15`:
`24 = b`
So now we know that the `y`-intercept is `24`.

Therefore, the slope-intercept form for this line is:
`y = -5x + 24`