Question

Find the equation of line b described below, in slope intercept form.Line a perpendicular to line bLine a passes through the points (1,-4) and (9,-6)Line b passes through the point (-6,-24)

Answer 1

First, we have to get the slope ( m ) of the Line a based on the two points given:

`m_A=(y_2-y_1)/(x_2-x_1)=(-6-(-4))/(9-1)=(-6+4)/(9-1)=-(2)/(8)=-(1)/(4)`

As they are perpendicular lines, the slope of Line a is the inverse of the slope of Line b with different sign. Therefore...

`m_B=(1)/(-m_A)=(1)/(-(-(1)/(4)))=4`

Finally, we find the constant of the equation using the point given of Line b.

`\begin{gathered} y_B=mx+b \\ b=y_B-mx=-24-(4\cdot-6)=-24-(-24)=-24+24=0 \\ b=0 \end{gathered}`

Answer:

`\begin{gathered} y_B=mx+b=4x+0 \\ y_{}=4x \end{gathered}`