Question

NEED ANSWER IMMEDIATELY!

I'm stupid.
what is the equation of a line that passes through the point (6, -8) and is perpendicular to the line whose equation is y = 2/3x + 3?

enter your answer in the box.

Answer 1

`\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\----------------------\\\\\text{The slope-intercept form:}\ y=mx+b.\\\\\text{We have}\ y=(2)/(3)x+3\to m_1=(2)/(3).\ \text{Therefore}\\\\m_2=-(1)/((2)/(3))=-(3)/(2)\\\\\text{We have the equation}\ y=-(3)/(2)x+b.`

`\text{Put the coordinates of the given point (6, -8) to the equation:}\\\\-8=-(3)/(2)(6)+b\\\\-8=-(3)(3)+b\\\\-8=-9+b\qquad\text{add 9 to both sides}\\\\1=b\to b=1\\\\Answer:\ \boxed{y=-(3)/(2)x+1}`