When given line $y = 2 x + 3$ $y=2x + 3$ and point (4,2), how would you find a parallel and a perpendicular line?

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Answer 1 · 2015-11-22T20:03:32

Let say that $y = m x + b$ $y=mx+b$ is the parallel to $y = 2 x + 3$ $y=2x+3$ from point $(4, 2)$ $(4,2)$

Hence $2 = 4 m + b$ $2=4m+b$ where $m = 2$ $m=2$ hence $b = - 6$ $b=-6$ so the line is

$y = 2 x - 6$ $y=2x-6$ .

The perpendicular line is $y = k x + c$ $y=kx+c$ where $k \cdot 2 = - 1 \Rightarrow k = - \frac{1}{2}$ $k*2=-1=>k=-1/2$ hence

$y = - \frac{1}{2} x + c$ $y=-1/2x+c$ .Because point $(4, 2)$ $(4,2)$ statisfies the equation we have that

$2 = - \frac{1}{2} \cdot 4 + c \Rightarrow c = 4$ $2=-1/2*4+c=>c=4$

Hence the perpendicular is $y = - \frac{1}{2} x + 4$ $y=-1/2x+4$

When given line y=2x + 3y=2x+3y=2x + 3 and point (4,2), how would you find a parallel and a perpendicular line?