Which of the lines is the equation of a line that passes through the point (3,6) and is perpendicular to the line 2x+4y=8?

Question

A. Y-6=-2(x-3)

b. Y=-2x+12

c. All of these

d. 2x+y-12=0

e. Y=2x

Answer 1

line ax + by = c, slope is -a/b

so for line 2x + 4y = 8, slope is -2/4 = -1/2

line perpendicular to that line has slope which is the negative reciprocal = 2.

in point slope format the equation of that line passing through (3,6) is:

y - 6 = 2(x-3), so it is not A, since that has -2 instead of 2 as the slope

solving for y:

y - 6 = 2x - 6

y = 2x , so it is E.

Answer 2

Lines that are perpendicular to each other have slopes that are the negative reciprocals of each other (if one has a slope of 2/3, then the other will have a slope of -3/2).

We can find the slope of 2x + 4y = 8 by putting it into slope-intercept form:

2x + 4y = 8

4y = -2x + 8

y = -2/4x + 8/4

y = -1/2x + 2

So the slope is -1/2

That means the slope of the line perpendicular to it is 2/1 or 2.

So we are looking for a line with a slope of 2 that goes through the point (3, 6) and we can use the point-slope form of a line to find it. The point-slope form is:

y - y₁ = m(x - x₁) where "m" is the slope and the point is (x₁, y₁) meaning x₁ = 3 and y₁ = 6 so:

y - 6 = 2(x - 3)

We can multiply this out to get:

y - 6 = 2x - 6 then add 6 to both sides to get y = 2x which is answer D