Question

Which function has the same y-intercept as the function?​

Answer 1

Answer:

$6x -7y = 21$

Step-by-step explanation:

The $y$-intercept of a line is the $y$ value when $x = 0$. In the equation $y = \frac23 x -3$, we can solve for its equation when we plug in $x = 0$.

Solving for $y$ when $x = 0$:

$y = \frac23 x -3 \\ y = \frac23 (0) -3 \\ y = -3$.

So the $y$-intercept of the equation $y = \frac23 x -3$ is $-3$.

To find what equation has the same $y$-intercept, we can do the same process for each equations given by the choices. However, I can see that the equation, $6x -7y = 21$, has the $y$-intercept. If in doubt, you can check for the solution below or solve each equations for yourself.

Solving for $y$ when $x = 0$:

$6x -7y = 21 \\ 6(0) -7y = 21 \\ 0 -7y = 21 \\ -7y = 21 \\ \frac{-7y}{-7} = \frac{21}{-7} \\ y = -3$