Question

Write an equation in slope-intercept form for the line that is perpendicular to y = −14x + 2 and passes through the point (-4, 3)

Answer 1

`k:y=m_1x+b_!\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1`

We have

`k:y=-14x+2`

`l:y=mx+b`

`l\ \perp\ k\ \iff\ -14m=-1\qquad|:(-14)\to m=(1)/(14)`

Therefore

`l:y=(1)/(14)x+b`

We know: the line l passes through the point (-4, 3).

Substitute the coordinates of the point to the equation of a line l:

`3=(1)/(14)\cdot(-4)+b\\\\3=(1)/(7)\cdot(-2)+b\\\\3=-(2)/(7)+b\qquad|+(2)/(7)\\\\b=3(2)/(7)`

Answer:
`y=(1)/(14)x+3(2)/(7)`