Question

Use the given conditions to write an equation for each line in general form.

Passing through (4, -7) and perpendicular to the line whose equation is x - 2y - 3 = 0.
Question 18 options:

6x - y - 1 = 0

4x + y + 1 = 0

7x - y + 2 = 0

2x + y - 1 = 0

Answer 1

It's the last choice:

2x + y - 1 = 0.

Explanation:

x - 2y - 3 = 0

Convert to slope-intercept form in order to find the slope:

-2y = -x + 3

y = 1/2x - 3/2

So the slope is 1/2. The slope of a line perpendicular to this is -1 / 1/2 = -2.

Using the point-slope form to find the required equation:

y - y1 = m(x - x1)

x = 4 and y = -7 so we have:

y + 7 = -2(x - 4)

y + 7 = -2x + 8

2x + y - 1 = 0 is the answer.