Passing through (-2,-11) and perpendicular to y=-1/4x+2 write a linear equation

The linear equation in slope-intercept form of the line that is perpendicular to y= -1/4x+2 and passes through (-2, -11) is: y = 4x - 3

Recall:

Given a line passes through (-2, -11) and is perpendicular to y = -1/4x + 2:

the slope (m) of the line will be the negative reciprocal to the slope of y = -1/4x + 2.

Write the equation in point-slope form using the point and the slope value of the perpendicular line, then rewrite in slope-intercept form.

Substitute (a, b) = (-2, -11) and m = 4 into y - b = m(x - a))

y - (-11) = 4(x - (-2))

y + 11 = 4(x + 2)

y + 11 = 4x + 8

y + 11 - 11 = 4x + 8 - 11

y = 4x - 3

Therefore, the equation in slope-intercept form of the line that is perpendicular to y= -1/4x+2 and passes through (-2, -11) is: y = 4x - 3

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y = 4x-3

To get this answer, first note that the slope of the given line y = -1/4x+2 is m = -1/4. We take the slope -1/4 and flip the fraction, and then flip the sign. So we end up with 4/1 or just 4. The perpendicular slope is 4, which is part of the answer we want.

We have y = mx+b turn into y = 4x+b. Plug in (x,y) = (-2,-11) and then solve for b

y = 4x+b

-11 = 4*(-2)+b replace x with -2, replace y with -11

-11 = -8+b

-11+8 = -8+b+8 add 8 to both sides

-3 = b

b = -3

So y = 4x+b turns into y = 4x-3 which is the answer