Question

Find the equation of a line that is perpendicular to 2x - y + 3 = 0 and has the same x-intercept as 2x + 6y + 20 = 0. Express your answer in slope-intercept form.

A) y = 2x + 3
B) y = -2x - 3
C) y = 2x - 3
D) y = -2x + 3

Answer 1

To find the equation of a line perpendicular to the given line and with the same x-intercept, we first find the slope of the given line, then determine the slope of the perpendicular line. We then find the x-intercept of the given line and use it to write the equation of the perpendicular line. The answer is option B) y = -2x - 10.

Step-by-step explanation:

To find the equation of a line that is perpendicular to 2x - y + 3 = 0 and has the same x-intercept as 2x + 6y + 20 = 0, we need to find the slope of the given line and then determine the slope of the perpendicular line. The given line can be rewritten in slope-intercept form as y = 2x + 3, so the slope of this line is 2. The slope of a line perpendicular to this line is the negative reciprocal of 2, which is -1/2. Now we know the slope of the perpendicular line and we can find its equation using the x-intercept from 2x + 6y + 20 = 0. To find the x-intercept, we set y = 0 and solve for x:

2x + 6(0) + 20 = 0

2x + 20 = 0

2x = -20

x = -10

So the x-intercept is -10. Therefore, the equation of the perpendicular line with the same x-intercept is y = -1/2x - 10. The answer is option B) y = -2x - 10.