Question

Which function has the same y-intercept as the function y=2 /3x-3?

Answer 1

Answer:

D has the same y-intercept

Step-by-step explanation:

y-intercept of the function in the question is -3.

A) 2/3 x + 3y = -3

Make y the subject

3y = -2/3x-3

y = -2/9-1

The y-intercept is -1; it is not the same.

B) -2/3 x + 3y = 6

Make y the subject

3y = 2/3x + 6

y = 2/9x + 2

The y-intercept is 2; it is not the same.

C) x + 4y = 12

Make y the subject

4y = -x + 12

y = -x + 3

The y-intercept is +3; it is not the same.

D) 6x - 7y = 21

Make y the subject

7y = 6x - 21

y = 6/7x - 3

The y-intercept is -3; it is the same.

Therefore, option D has the same y-intercept as the function given in the question.

Answer 2

Answer:

Option D.

Step-by-step explanation:

The given function is

$y=\frac{2}{3}x-3$

Substitute x=0 in the given function to find the y-intercept.

$y=\frac{2}{3}(0)-3=-3$

The y-intercept of the given function is -3. We need to find the equation whose y-intercept is -3.

Substitute x=0 in the given each of the equations to find the y-intercepts of those equation.

First equation is

$\frac{2}{3}x+3y=-3$

$\frac{2}{3}(0)+3y=-3$

$3y=-3$

$y=-1$

y-intercept is -1.

Second equation is

$-\frac{2}{3}x+3y=6$

$-\frac{2}{3}(0)+3y=6$

$3y=6$

$y=2$

y-intercept is 2.

Third equation is

$x+4y=12$

$(0)+4y=12$

$4y=12$

$y=3$

y-intercept is 3.

Fourth equation is

$6x-7y=21$

$6(0)-7y=21$

$-7y=21$

$y=-3$

y-intercept is -3.

Therefore, the correct option is D.