Question

How do you write the equation in slope intercept form given `y-(-4)=-1(x-6)`?

Answer 1

`y=(-1)x+2`

Explanation:

Remember that the general slope-intercept form is
`color(white)("XXX")y=color(green)(m)x+color(red)(b)`
for a line with slope `color(green)(m)` and y-intercept `color(red)(b)`

Given
`color(white)("XXX")y-(-4)=-1(x-6)`

Add `(-4)` to both sides to isolate the `y` on the left side
`color(white)("XXX")y=-1(x-6)+(-4)`

Simplify the right side
`color(white)("XXX")y=-x+6-4`

`color(white)("XXX")y=color(green)(""(-1))x+color(red)(2)`
which is the slope-intercept form
for a line with slope `color(green)(""(-1))` and y-intercept `color(red)(2)`

Here is the graph of the original equation which supports our conclusion:
graph{y-(-4)=-1(x-6) [-4.27, 8.214, -2.124, 4.116]}