Question

Identify an equation in point-slope form for the line perpendicular to

y=-4x – 1 that passes through (-2,7).

Answer 1

`\large\boxed{y=(1)/(4)x+(15)/(2)}`

Explanation:

`\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\==================================`

`\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-(1)/(-4)=(1)/(4).\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=(1)/(4)x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=(1)/(4)(-2)+b\\\\7=-(1)/(2)+b\qquad\text{add}\ (1)/(2)\ \text{to both sides}\\\\7(1)/(2)=b\to b=7(1)/(2)=(7\cdot2+1)/(2)=(15)/(2)\\\\\text{Finally:}\\\\y=(1)/(4)x+(15)/(2)`