Question

which functional has the samey-intercept as the function
y=\frac{2}{3}x-3?

A. x+4y=12
B. -\frac{2}{3}x+3y=6
C. \frac{2}{3}x+3y=-3
D. 6x-7y=21

Answer 1

To find the y-intercept of the function y = (2/3)x - 3, we need to set x = 0 and solve for y:

y = (2/3)(0) - 3
y = 0 - 3
y = -3

So, the y-intercept is -3.

Now, we need to look at each answer choice and find the one that has the same y-intercept of -3.

A. x + 4y = 12
If x = 0, then 4y = 12 and y = 3, so the y-intercept is 3, not -3. This is not the correct answer.

B. -(2/3)x + 3y = 6
If x = 0, then 3y = 6 and y = 2, so the y-intercept is 2, not -3. This is not the correct answer.

C. (2/3)x + 3y = -3
If x = 0, then 3y = -3 and y = -1, so the y-intercept is -1, not -3. This is not the correct answer.

D. 6x - 7y = 21
If x = 0, then -7y = 21 and y = -3, so the correct answer is D.

Therefore, the function represented by D, 6x - 7y = 21, has the same y-intercept as the function y = (2/3)x - 3.