Question

Choose the equation of the line passing through the point (-1, 7) and perpendicular to y = -one fourthx - 5.

y = -4x - 11

y = -4x - 3

y = 4x + 11

y = 4x + 3

Answer 1

the given line is
\[y=-\frac{1}{4}x-5\]
since it is already in slope intercept form, y=mx+b, it is easy to determine the slope of this line
m= slope, so our slope is -1/4

now we want to find a line perpendicular to this line. the slope of a perpendicular line is always the negative reciprocal

since our original slope is -1/4, we find the negative of it which is 1/4, then we find the recipocal which is 4

now we have the slope of the perpendicular line

we want this perpendicular line to travel through the point (-1,7)

so we substitute these values into the point slope form and solve for slope intercept form
\[y-y_1=m(x-x_1)\]