Question

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

Answer 1

`6x -7y = 21`

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 \\ (-7y)/(-7) = (21)/(-7) \\ y = -3`