Question

What is an equation of the line that passes through the point (4,-6) and has a slope of -3?

Answer 1

`y=-3x+6`

Explanation:

.

The equation of a straight line has the form:

`y=mx+b` where `m` is the slope and `b` is the `y`-inercept, i.e. where the line crosses the `y`-axis.

Therefore, the equation of this line will be:

`y=-3x+b` because our slope is `-3`.

Now we plug in the coordinates of the given point the line goes through, and solve for `b`:

`-6=-3(4)+b`

`-6=-12+b`

`b=6`

Therefore, the equation is:

`y=-3x+6`

Answer 2

`y=-3x+6`

Explanation:

Slope`=-3` and passes through point `(4,-6)`.

Using the point-slope general formula, of a line,

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

Substitute the coordinates into `x_1` and `y_1`,

`y-(-6)=-3(x-4)`

Simplify,

`y+6=-3x+12`

Subtract `6` from both sides,

`y=-3x+6rarr` answer

Check:

graph{-3x+6 [-10, 10, -5, 5]}
`y=-3x+6`