Question

10.Write the equation in slope-intercept form for the line that passes through the given pointand is perpendicular to the given equation.6x + 3y = -9 and passes through (-2, 2)

Answer 1

Let first put the equation of the first line in the form of slope intercept

`\begin{gathered} 6x+3y=-9\rightarrow \\ y=(-9-6x)/(3)=-3-2x \end{gathered}`

So it's slope is -2, so the new slope is

`m=-(1)/(-2)=(1)/(2)`

Having the slope, we have that

`\begin{gathered} y-2=(1)/(2)(x+2)=(1)/(2)x+1 \\ y=(1)/(2)x+1+2=(1)/(2)x+3 \end{gathered}`

so the equation is

`y=(1)/(2)x+3`