Question

write an equation in slope intercept for the lune that passes through the point (0,2) and is parallel to the graph of the equation y=-5x+8

Answer 1

If they are parallel:

$m1=m2$

Since the slope for y=-5x+8​ is m1=-5:

$m2=-5$

Let:

(x1,y1)=(0,2)

Using the point-slope equation:

$\begin{gathered} y-y1=m(x-x1) \\ y-2=-5(x-0) \\ y-2=-5x \\ y=-5x+2 \end{gathered}$

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If is perpendicular to the line equation y=1/2x-3:

$\begin{gathered} m1\times m2=-1 \\ \text{Where:} \\ m1=\frac{1}{2} \\ \frac{1}{2}\times m2=-1 \\ m2=-2 \end{gathered}$

Let:

(x1,y1)=(-5,2)

Using the point-slope equation:

$\begin{gathered} y-y1=m(x-x1) \\ y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-8 \end{gathered}$