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:
[tex]y-y_1=m(x-x_1)[/tex]
Using the point and slope provided,
[tex](x,y)=(-3,5);m=-2[/tex]
we can substitute into the form:
[tex]\begin{gathered} y-5=-2(x-(-3)) \\ \\ y-5=-2(x+3) \end{gathered}[/tex]
To write it into slope-intercept form, we need to simplify the right-hand side, then isolate the y-variable.
Apply the distributive property:
[tex]\begin{gathered} y-5=-2(x)-2(3) \\ \\ y-5=-2x-6 \end{gathered}[/tex]
Add 5 to both sides:
[tex]\begin{gathered} y-5+5=-2x-6+5 \\ \\ y=-2x-1 \end{gathered}[/tex]
So, the slope intercept form is
[tex]\boxed{y=-2x-1}[/tex]
