Question

What’s the line contains the point (-5,7) and is perpendicular to a line with a slope of 5/3

Answer 1

`\large\boxed{y=-(3)/(5)+4}`

Explanation:

`\text{Let}\ k:y=m_1x+b_1,\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\===========================\\\\\text{We have}\ m_1=(5)/(3),\ \text{therefore}\ m_2=-(1)/((5)/(3))=-(3)/(5).\\\\l:y=-(3)/(5)x+b\\\\\text{Put the coordinates of the point (-5, 7) to the equation of a line }\ l:\\\\7=-(3)/(5)(-5)+b\\\\7=3+b\qquad\text{subtract 3 from both sides}\\\\4=b\to b=4\\\\\text{Fimally we have the equation:}\\\\l:y=-(3)/(5)+4`

Answer 2

Slope. perp. -3/5

y - 7 = -3/5(x + 5)

y - 7 = -3/5x - 3

y = -3/5x + 4