Question

Which function has the same y-intercept as the function $y=\frac{2x}{3}-3$.

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

Answer 1

The correct option is C

$6x-7y=21$

The explanation for the correct option :

Step 1: y-intercept of $\mathit{y}\mathbf{=}\frac{\mathbf{2}\mathbf{x}}{\mathbf{3}}\mathbf{-}\mathbf{3}$

putting $x=0$ we get

$y=-3$

Step 2: y-intercept of $\frac{2x}{3}+3y=-3$

putting $x=0$ in $\frac{2x}{3}+3y=-3$ we get

$y=-1$

Step 3: y-intercept of $-\frac{2x}{3}+3y=6$

putting $x=0$ in $-\frac{2x}{3}+3y=6$ we get

$y=2$

Step 4: y-intercept of $6x-7y=21$

putting $x=0$ in $6x-7y=21$ we get

$y=-3$

Step 5: y-intercept of $x+4y=12$

putting $x=0$ in $x+4y=12$ we get

$y=3$

Hence, the function $\mathbf{6}\mathit{x}\mathbf{-}\mathbf{7}\mathit{y}\mathbf{=}\mathbf{21}$ has the same y-intercept as the function$\mathit{y}\mathbf{=}\frac{\mathbf{2}\mathbf{x}}{\mathbf{3}}\mathbf{-}\mathbf{3}$.

Therefore, the correct option is $\left(C\right)$.

The explanation for the incorrect option :

The obtained function is $y=\frac{2\mathrm{x}}{3}-3$ which is not equivalent to option $\left(A\right)$, option$\left(B\right)$, option$\left(D\right)$.

Hence , option$\left(A\right)$, option$\left(B\right)$, option$\left(D\right)$ all are incorrect.