Question

Need answers asap please

Answer 1

An equation in point-slope form that passes through point P(a,b) is as follows:

y-b=m(x-a)   where m=slope, a,b are coordinates of point P.

For a line to pass through P(4,-8)
the equation will look like:
y-(-8) = m(x-4)
simplify left side
y+8=m(x-4)

The given equation has a slope of m=-1/2, so the slope of a line perpendicular to it has a slope of -1/m = -1/(-1/2)=+2

Now go through the answer choices:
a. y+8=2(x-4)  => passes through P(4,-8) and has a slope of 2.  so TRUE
b. y-4=2(x+8)  => has a slope of 2, but passes through (-8,4), which is not P so FALSE
c. y+8=(1/2)(x-4) => passes through P(4,-8), but has the wrong slope (a reflection, not perpendicular)  so FALSE
d. y-8=(1/2)(x+4) => passes through a wrong point (-4,8) and has the reflected slope (not perpendicular)  so FALSE