Question

xleb123 · Accepted Answer

To find an equation of a line perpendicular to the graph of

y = \frac{1}{4} x + 5

and passing through the point

(- 3, 8)

, we need to determine two things: the slope of the perpendicular line and its y-intercept.
The given equation is in slope-intercept form

y = m x + b

, where

m

represents the slope of the line. Since the given line has a slope of

\frac{1}{4}

, the perpendicular line will have a slope that is the negative reciprocal of

\frac{1}{4}

.
The negative reciprocal of

\frac{1}{4}

is

- \frac{4}{1} = - 4

. Therefore, the perpendicular line has a slope of

- 4

.
Now, using the point-slope form of a line, we can write the equation of the perpendicular line:

y - y_{1} = m (x - x_{1})

where

(x_{1}, y_{1})

represents the given point

(- 3, 8)

, and

m

is the slope of the perpendicular line (

- 4

).
Substituting the values into the equation:

y - 8 = - 4 (x - (- 3))

Simplifying:

y - 8 = - 4 (x + 3)

y - 8 = - 4 x - 12

To obtain the equation in slope-intercept form, we can isolate

y

on one side:

y = - 4 x - 12 + 8

y = - 4 x - 4

Therefore, the equation of the line perpendicular to

y = \frac{1}{4} x + 5

and passing through the point

(- 3, 8)

is

y = - 4 x - 4

.

Answered question