Question

Function A is defined as 2x - 3y = 6, and function B is defined as -x + 4y = -12. What is the positive difference between the two x-intercepts?

a) 2
b) 4
c) 6
d) 8

Answer 1

The x-intercepts for functions A (2x - 3y = 6) and B (-x + 4y = -12) are (3,0) and (12,0), respectively. The positive difference between these x-intercepts is 9, an option not listed in the question, suggesting an error in the options.

Step-by-step explanation:

To find the positive difference between the two x-intercepts of the given functions A and B, we first need to solve for the x-intercepts. An x-intercept occurs where y is equal to 0.

For function A (2x - 3y = 6), setting y to 0 gives us:

2x - 3(0) = 6

2x = 6

x = 3

So the x-intercept for function A is at (3,0).

For function B (-x + 4y = -12), setting y to 0 gives us:

-x + 4(0) = -12

-x = -12

x = 12

The x-intercept for function B is at (12,0).

To find the positive difference between the x-intercepts of functions A and B, we subtract the x-value of function A's intercept from the x-value of function B's intercept:

12 - 3 = 9

The positive difference between the two x-intercepts is 9, which is not one of the options provided in the question. Therefore, there may be an error in the provided options.