Question

What is an equation of the line that is perpendicular to y=−2/3x+5 and passes through the point (2, 11) ?

Answer 1

`\large\boxed{y=(3)/(2)x+8}`

Explanation:

`\text{The slope-intercept form:}`

`y=mx+b\\\\m - slope\\b - y-intercept`

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

`\text{We have}\ y=-(2)/(3)x+5\to m_1=-(2)/(3).\\\\\text{Therefore}\ m_2=-(1)/(-(2)/(3))=-\left(-(3)/(2)\right)=(3)/(2)\\\\\text{We have the equation}\ y=(3)/(2)x+b.\\\\\text{Put the coordinates of the point (2, 11) to the equation and calculate b}:\\\\11=(3)/(2)(2)+b\\\\11=3+b\qquad\text{subtract 3 from both sides}\\\\8=b\to b=8\\\\\text{Finally we have}\ y=(3)/(2)x+8.`