Question

How do you write an equation in slope intercept form of a line containing the coordinates (4,-5) with a slope of -6?

Answer 1

`y=-6x+19`

Explanation:

With the point `(color(red)(4),color(blue)(-5))` and a slope of `(color(green)(-6))`
we can write the equation (initially) in slope-point form:
`color(white)("XXX")y-(color(blue)(-5))=(color(green)(-6))(x-color(red)(4))`
then simplifying:
`color(white)("XXX")y+5=-6x+24`
or
`color(white)("XXX")y=(color(green)(-6))x+color(purple)(19)`
which is the slope-intercept form with slope `(color(green)(-6))` and y-intercept `color(purple)(19)`

graph{(-6x+19-y)((x-4)^2+(y+5)^2-0.01)=0 [-5.79, 14.21, -7.525, 2.475]}