Question

Write an equation of a line that goes through point `(4,-5)` and is parallel to line `y=-3x+8`.

Answer 1

A line that is parallel to `y = -3x + 8` will have the same slope. The slope of `y = -3x + 8` is `-3`.
We can use the point-slope form of a line to find the equation of the line that goes through `(4, -5)` with a slope of `-3`:

y - y1 = m(x - x1)

Substituting `(4, -5)` for `(x1, y1)` and `-3` for `m`, we have:

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

Simplifying the equation gives:

y + 5 = -3x + 12

Rearranging the equation to slope-intercept form, we have:

y = -3x + 7

Therefore, the equation of the line that goes through point `(4, -5)` and is parallel to line `y = -3x + 8` is `y = -3x + 7`.