Answer: D

Translating a graph up $3$ units replaces $y$ with $y - 3$: $2x + 5(y - 3) = 30$, or $2x + 5y = 45$. At the $x$-intercept, $y = 0$, so $2x = 45$ and $x = 22.5$. As a check, the original line has slope $-\frac{2}{5}$ and $x$-intercept $15$, and raising it $3$ units moves the $x$-intercept $3 \div \frac{2}{5} = 7.5$ units to the right.

Choice C moves the $x$-intercept $3$ units to the right, but because the slope is $-\frac{2}{5}$, a vertical shift of $3$ moves the $x$-intercept $7.5$ units.

Why the other choices are wrong

• A. 15 is the x-intercept of the original graph, before the translation.
• B. This adds 3 to the constant, giving 2x + 5y = 33. Replacing y with y - 3 adds 5 × 3 = 15 to the constant.
• C. This moves the x-intercept 3 units right, which is a horizontal shift. Moving this line up 3 units moves its x-intercept 7.5 units right.