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=-(1)/(m) \\ \Rightarrow m_p=-(1)/(-2)=(1)/(2) \\ m_p=(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=(1)/(2) \\ (x,y)=(-3,-2) \\ y=mx+b \\ \Rightarrow-2=(1)/(2)(-3)+b \\ \Rightarrow-2+(3)/(2)=b \\ \Rightarrow b=-(1)/(2) \end{gathered}`

Therefore, the equation in slope-intercept form is:

`y=(1)/(2)x-(1)/(2)`