Write an equation of a line passing through (8, 2), perpendicular to 4x−y=12

Kevin Charles
2022-10-14
Answered

Write an equation of a line passing through (8, 2), perpendicular to 4x−y=12

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megagoalai

Answered 2022-10-15
Author has **22** answers

Comparing with the equation of line in slope-intercept form y=mx+c

we get the slope of the line 4x−y=12 or y=4x−12 as ${m}_{1}=4$

The slope of the perpendicular line is ${m}_{2}=-\frac{1}{{m}_{1}}=-\frac{1}{4}\therefore$

The equation of line passing through (8,2) is $y-{y}_{1}={m}_{2}(x-{x}_{1})\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-2=-\frac{1}{4}(x-8)\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=-\frac{1}{4}x+4$

we get the slope of the line 4x−y=12 or y=4x−12 as ${m}_{1}=4$

The slope of the perpendicular line is ${m}_{2}=-\frac{1}{{m}_{1}}=-\frac{1}{4}\therefore$

The equation of line passing through (8,2) is $y-{y}_{1}={m}_{2}(x-{x}_{1})\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-2=-\frac{1}{4}(x-8)\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=-\frac{1}{4}x+4$

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