A line has an x-intercept of 5 and a y-intercept of -10. What is the slope of the line?

The intercepts give two points on the line: the $x$-intercept 5 is $(5, 0)$, and the $y$-intercept $-10$ is $(0, -10)$. The slope is rise over run: $\frac{0 - (-10)}{5 - 0} = \frac{10}{5} = 2$. The line rises to the right, so a positive slope makes sense. A common wrong answer is $-2$, which comes from a sign error when subtracting $-10$. Another is $\frac{1}{2}$, which inverts the ratio, giving run over rise. A third is $-\frac{1}{2}$, which combines both errors. Check with the equation $y = 2x - 10$, which gives 0 at $x = 5$.