Question

Identify an equation in point-slope form for the line perpendicular to (y = -1/2x + 11) that passes through (4,8).

a) (y - 8 = 2(x - 4))
b) (y - 8 = -2(x - 4))
c) (y + 8 = 2(x - 4))
d) (y + 8 = -2(x - 4))

Answer 1

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The correct equation in point-slope form for the line perpendicular to y = -1/2x + 11 that passes through (4,8) is (y - 8) = 2(x - 4), which corresponds to option a.

Step-by-step explanation:

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The original line is given as y = -1/2x + 11, so its slope is -1/2. The negative reciprocal of -1/2 is 2. Therefore, the slope of the perpendicular line will be 2.

Next, we can use the point-slope form of a linear equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Plugging in the values (4,8) for (x₁, y₁) and 2 for m, we get the equation (y - 8) = 2(x - 4).

Therefore, the correct equation in point-slope form for the line perpendicular to y = -1/2x + 11 that passes through (4,8) is (y - 8) = 2(x - 4), which corresponds to option a.