Question

Two lines with nonzero slope and the same y-intercept have the property that the sum of their slopes is 0. What is the sum of the x-coordinates of their y-intercepts?

a) 0
b) 1
c) -1
d) 2

Answer 1

The sum of the x-coordinates of the y-intercepts of the two lines is 1.

Step-by-step explanation:

The sum of the x-coordinates of their y-intercepts is b) 1.

To find the sum of the x-coordinates of their y-intercepts, we need to first identify the y-intercept of each line. Since both lines have the same y-intercept, the y-intercept will be a constant value. Let's call this constant value 'a'.

The equation of the first line is y = mx + a, and the equation of the second line is y = nx + a. Given that the sum of their slopes (m+n) is 0, we can write the equation m + n = 0. From here, we can solve for m or n, let's solve for m.

m + n = 0

m = -n.

Now, let's calculate the x-coordinate of the y-intercept for the first line using the given point (1, 0.1).

y = mx + a

0.1 = m(1) + a.

Substituting m = -n, we get

0.1 = -n(1) + a.

0.1 = -n + a.

Since the y-intercept is the value of y when x = 0, we can set x = 0 in the equation to find a.

0.1 = a.

Therefore, the y-intercept for both lines is a = 0.1, and the sum of the x-coordinates of their y-intercepts is 0 + 0 = 0.1.