A line has an x-intercept of 4 and a y-intercept of -6. What is the slope of the line?

The intercepts give two points on the line: the $x$-intercept 4 is the point $(4, 0)$ and the $y$-intercept $-6$ is the point $(0, -6)$. The slope is rise over run: $\frac{0 - (-6)}{4 - 0} = \frac{6}{4} = \frac{3}{2}$, choice B. The line rises as it moves right, so the slope is positive. Choice A ($-\frac{3}{2}$) has the wrong sign, which happens when the subtraction of $-6$ is mishandled. Choice C ($\frac{2}{3}$) inverts the ratio into run over rise. Choice D ($-\frac{2}{3}$) combines both errors. Check with the equation $y = \frac{3}{2}x - 6$, which gives 0 at $x = 4$.