Question

I need help with getting the answer to this question

Answer 1

In this problem, we want to rewrite an equation from point-slope form to slope-intercept form, given a point and the slope.

In point-slope form, we have:

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

Using the point and slope provided,

`(x,y)=(-3,5);m=-2`

we can substitute into the form:

`\begin{gathered} y-5=-2(x-(-3)) \\ \\ y-5=-2(x+3) \end{gathered}`

To write it into slope-intercept form, we need to simplify the right-hand side, then isolate the y-variable.

Apply the distributive property:

`\begin{gathered} y-5=-2(x)-2(3) \\ \\ y-5=-2x-6 \end{gathered}`

Add 5 to both sides:

`\begin{gathered} y-5+5=-2x-6+5 \\ \\ y=-2x-1 \end{gathered}`

So, the slope intercept form is

`\boxed{y=-2x-1}`