Question

Y=-1/2x+11 that passes through (4,-8)

Answer 1

A line in point-slope form has the equation

y = mx + b

where m=slope (increase in y for unit increase in x), and

b=y-intercept (value of y where line cuts y-axis)

The original line is

y=(-1/2)x + 11

so

slope = m = -1/2

Any line perpendicular to a line with slope m has a slope of m1=-1/m

So the slope m1 of the required line

m1 = -1 / (-1/2) = +2

and the required line therefore has an equation of

y=2x+b

Knowing that the line passes through P1=(x1, y1)=(4,-8), we can find b using the point slope form of a line with slope m : (y-y1) = m(x-x1)

where m=+2 as found above.

Substituting values, m=+2, x1=4, y1= -8

y-(-8) = +2(x--4)

simplify

y+8 = 2x-8

=>

y=2x-16 (in point slope form)