Question

What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5 x + 10 and passes through the point (15, –5)?

The equation of the line in slope-intercept form is y = -5/3 x +

Answer 1

`\large\boxed{y-intercept=20}`

Explanation:

`\text{Let}\ k:y=_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=(3)/(5)x+10\to m_1=(3)/(5).\\\\\text{Therefore}\ m_2=-(1)/((3)/(5))=-(5)/(3).\\\\\text{The equation of the searched line:}\ y=-(5)/(3)x+b.\\\\\text{The line passes through }(15,\ -5).`

`\text{Put thecoordinates of the point to the equation.}\ x=15,\ y=-5:\\\\-5=-(5)/(3)(15)+b\\\\-5=(-5)(5)+b\\\\-5=-25+b\qquad\text{add 25 to both sides}\\\\b=20\\\\\boxed{y=-(5)/(3)x+20}`