Question

What is the equation of a line that passes through the point (1, 8) and is perpendicular to the line whose equation is y = x/2 + 3 ?

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Answer 1

y = - 2x + 10

the equation y = $\frac{1}{2}$ x + 3 is in slope- intercept form

with slope m = $\frac{1}{2}$

given a line with slope m then the slope of a line perpendicular to it is m₂ = - $\frac{1}{m}$

perpendicular slope = - 2

partial equation is y = - 2x + c

to find c substitute (1, 8 ) into the partial equation

8 = - 2 + c ⇒ c = 8 + 2 = 10

y = - 2x + 10 ( equation in slope-intercept form )