Question

Write an equation for a line perpendicular to y = -2 x -4 and passing through the point (2,5)

Answer 1

First we need to find the slope.
Do you know the slope of the equation : y = -2x - 4 ??

Answer 2

In y = mx + b form, the slope can be found in the m position. Therefore, the slope of : y = -2x - 4 would be -2.
We are looking for a perpendicular line...so we need the negative reciprocal slope of -2. To find the negative reciprocal slope, " flip " the slope, and change the sign. So the negative reciprocal slope of -2 (or -2/1) is 1/2....see how I flipped the slope and changed the sign ?
Now we will use y = mx + b, and since we already know the slope(m) is 1/2, we need to find the y intercept (b)

y = mx + b -- we are looking for b, the y intercept
slope(m) = 1/2
(2,5)....x = 2 and y = 5
now we sub
5 = 1/2(2) + b
5 = 1 + b
5 - 1 = b
4 = b

Therefore our perpendicular equation is : y = 1/2x + 4