Question

Which of the following lines has the same y-intercept as $y=\frac{x}{2}-3?$

• A. $x+2=3y$
• B. $y+3=x+2$
• C. $y+3=2x$
• D. $\frac{y}{2}=x-3$

Answer 1

The correct option is C $y+3=2x$

The given equation is $y=\frac{x}{2}-3$ .......... $\left(i\right)$

Equation in slope-intercept form is given by $y=mx+c$, where $m$ is the slope and $c$ is the $y-$intercept.

Comparing $\left(i\right)$ with slope-intercept form we get $m=\frac{1}{2}$ and $c=-3$ is the $y-$intercept.

In option A, $y=\frac{x}{3}+\frac{2}{3}⟹y-$intercept is $\frac{2}{3}$

In option B, $y=x-1⟹y-$intercept is $-1$

In option C, $y=2x-3⟹y-$intercept is $-3$ which is same as of $\left(i\right)$

In option D, $y=2x-6⟹y-$intercept is $-6$

Thus, the equation $y+3=2x$ has the same $y-$intercept as $\left(i\right)$

Hence, option C is correct.