# 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)

Francis Oliver 2022-10-26 Answered
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)
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megagoalai
Given a line with slope m then the slope of a line perpendicular to it is
$•x{m}_{\text{perpendicular}}=-\frac{1}{m}$
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
$⇒{m}_{\text{perpendicular}}=-\frac{1}{-4}=\frac{1}{4}$
$⇒y=\frac{1}{4}x+b←\text{is the partial equation}$
to find b substitute (2,6) into the partial equation
$6=\frac{1}{2}+b⇒b=\frac{12}{2}-\frac{1}{2}=\frac{11}{2}$
$⇒y=\frac{1}{4}x+\frac{11}{2}←\text{in slope-intercept form}$