Respuesta :

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]

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