Line $\ell$ is perpendicular to the line with equation $y=x-3$. Line $\ell$ has the same $x$-intercept as the line with equation $y=x-3$. The $y$-intercept of line $\ell$ is
(A) -3
(B) $\frac{1}{3}$
(C) 3
(D) -1
(E) 0
The line with equation $y=x-3$ has slope 1 .

To find the $x$-intercept of the line with equation $y=x-3$, we set $y=0$ and solve for $x$ to obtain $x-3=0$ or $x=3$. Thus, line $\ell$ also has $x$-intercept 3 .

Further, since the two lines are perpendicular, the slopes of the two lines have a product of -1 , which means that the slope of $\ell$ is -1 .

Line $\ell$ has slope -1 and passes through $(3,0)$.

This means that $\ell$ has equation $y-0=-1(x-3)$ or $y=-x+3$.

Therefore, the $y$-intercept of line $\ell$ is 3 .

ANSWER: $(\mathrm{C})$