Question

Choose the equation of the line passing through the point (-2, 4) and perpendicular to y = -negative one halfx + 4.

Answer 1

y = -1/2x + 4
the slope here is -1/2

However, we are looking for a perpendicular slope. A perpendicular slope is the negative reciprocal of the slope given. So we need the negtative reciprocal of -1/2. To find the negative reciprocal, we " flip " the slope and change the sign. So the negative reciprocal of -1/2 is 2/1, or just 2 (see how I flipped the slope and changed the sign)

Now we can use y = mx + b....m being the slope and b is the y intercept
we already know the slope, so we have to find the y intercept (b).
so we sub
y = mx + b
slope(m) = 2 (we need to use the perpendicular slope)
(-2,4)...x = -2 and y = 4

y = mx + b
4 = 2(-2) + b
4 = -4 + b
4 + 4 = b
8 = b

so your perpendicular line is : y = 2x + 8

Answer 2

ok so if you want it to be perpendicular you your slope has to be the negative reciprocal. so that makes -1/2x into a -(-2x) and two negatives=positive so your new slope is going to be 2x. Now in order to see whether the line passes through a certain point you can either a.) graph it, or you can b.) solve the equation. Because it has to be perpendicular you cannot change the slope so now you have to change your intercept which is your b value (y=mx+b). The b value will either raise or lower your line so that it crosses at a certain point. Now plug in the values into the equation and solve for b. Your final result will be y=2x+8