Question

Write the slope-intercept form of the equation that passes through the point (-3, 5) and is perpendicular to the line y = 1/5x + 10 y = 5x + 10 y = -1/5x + 22/5 y = 1/5x + 28/5 y = -5x - 10

Answer 1

y = -5x - 10

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=(1)/(5)x+10\to m_1=(1)/(5)\\\\\text{Therefore}\ m_2=-(1)/((1)/(5))=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10`