Question

Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given équation.9.(-3, -2), y = -2x+ 4

Answer 1

Given the equation y=-2x+4, we can easily find the slope of the perpendicular line by calculating the inverse negative of the slope. This is:

$\begin{gathered} y=-2x+4 \\ m=-2 \\ m_p=-\frac{1}{m} \\ \Rightarrow m_p=-\frac{1}{-2}=\frac{1}{2} \\ m_p=\frac{1}{2} \end{gathered}$

Now that we have the slope, we can ouse the equation slope-intercept to find the intercept b using the point (-3,-2):

$\begin{gathered} m_p=\frac{1}{2} \\ (x,y)=(-3,-2) \\ y=mx+b \\ \Rightarrow-2=\frac{1}{2}(-3)+b \\ \Rightarrow-2+\frac{3}{2}=b \\ \Rightarrow b=-\frac{1}{2} \end{gathered}$

Therefore, the equation in slope-intercept form is:

$y=\frac{1}{2}x-\frac{1}{2}$