Francis Oliver

2022-10-26

Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)

megagoalai

Beginner2022-10-27Added 22 answers

Given a line with slope m then the slope of a line perpendicular to it is

$\u2022{x}{m}_{{\text{perpendicular}}}=-\frac{1}{m}$

the equation of a line in slope-intercept form is

y=mx+b

where m is the slope and b the y-intercept

y=−4x is in this form

with slope m=−4

$\Rightarrow {m}_{{\text{perpendicular}}}=-\frac{1}{-4}=\frac{1}{4}$

$\Rightarrow y=\frac{1}{4}x+b\leftarrow {\text{is the partial equation}}$

to find b substitute (2,6) into the partial equation

$6=\frac{1}{2}+b\Rightarrow b=\frac{12}{2}-\frac{1}{2}=\frac{11}{2}$

$\Rightarrow y=\frac{1}{4}x+\frac{11}{2}\leftarrow {\text{in slope-intercept form}}$

$\u2022{x}{m}_{{\text{perpendicular}}}=-\frac{1}{m}$

the equation of a line in slope-intercept form is

y=mx+b

where m is the slope and b the y-intercept

y=−4x is in this form

with slope m=−4

$\Rightarrow {m}_{{\text{perpendicular}}}=-\frac{1}{-4}=\frac{1}{4}$

$\Rightarrow y=\frac{1}{4}x+b\leftarrow {\text{is the partial equation}}$

to find b substitute (2,6) into the partial equation

$6=\frac{1}{2}+b\Rightarrow b=\frac{12}{2}-\frac{1}{2}=\frac{11}{2}$

$\Rightarrow y=\frac{1}{4}x+\frac{11}{2}\leftarrow {\text{in slope-intercept form}}$

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