Question

Find the equation of the line which passes through the point (−3, 5) and is perpendicular to the line 4x + 3y = 6. Express your answer in slope-intercept form.

Answer 1

`y=(3)/(4)x+7(1)/(4)`

Explanation:

`k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1`

Let
`k:4x+3y=6\to 3y=-4x+6\ \ \ \ |:3\\\\y=-(4)/(3)x+2\\\\m_1=-(4)/(3)`

`l:y=m_2x+b\\\\l\ \perp\ k\ \iff\ -(4)/(3)m_2=-1\qquad|\cdot\left(-(3)/(4)\right)\\\\m_2=(3)/(4)\\\\l:y=(3)/(4)x+b`

The line l passes through the point (-3, 5).

Substitute the coordinates of the point to the equation of the function l:

`5=(3)/(4)(-3)+b\\\\5=-(9)/(4)+b\\\\5=-2(1)/(4)+b\qquad|+2(1)/(4)\\\\b=7(1)/(4)`

Finally
`l:y=(3)/(4)x+7(1)/(4)`