Answer:
[tex]6x -7y = 21[/tex]
Step-by-step explanation:
The [tex]y[/tex]-intercept of a line is the [tex]y[/tex] value when [tex]x = 0[/tex]. In the equation [tex]y = \frac23 x -3 \\[/tex], we can solve for its equation when we plug in [tex]x = 0[/tex].
Solving for [tex]y[/tex] when [tex]x = 0[/tex]:
[tex]y = \frac23 x -3 \\ y = \frac23 (0) -3 \\ y = -3[/tex].
So the [tex]y[/tex]-intercept of the equation [tex]y = \frac23 x -3 \\[/tex] is [tex]-3[/tex].
To find what equation has the same [tex]y[/tex]-intercept, we can do the same process for each equations given by the choices. However, I can see that the equation, [tex]6x -7y = 21[/tex], has the [tex]y[/tex]-intercept. If in doubt, you can check for the solution below or solve each equations for yourself.
Solving for [tex]y[/tex] when [tex]x = 0[/tex]:
[tex]6x -7y = 21 \\ 6(0) -7y = 21 \\ 0 -7y = 21 \\ -7y = 21 \\ \frac{-7y}{-7} = \frac{21}{-7} \\ y = -3[/tex]
