Line l is perpendicular to a line m with equation −4x+12y=−20 . Line l intersects line m at (−10,−5) . The equation of line l, in slope-intercept form, is

Question

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Answer 1

-4x + 12y = -20

12y = 4x - 20

y = (1/3)x - 5/3   This line has a slope of 1/3.

Perpendicular lines have slopes that are negative reciprocals of each other. So, line l will have a slope of -3.

Now you have a point (-10,-5) and a slope (-3). so, use the Point Slope form of the equation of a line.

y - y₁ = m(x - x₁)

y + 5 = -3(x + 10)

y + 5 = -3x - 30

y = -3x - 35