Lesson 4-2: Slope of a Line — Practice Questions

1. 1. A mountain pass rises 0.6 miles over a horizontal distance of 26 miles. A driveway rises 12 feet over a horizontal distance of 150 feet. Which is steeper? (Note: 1 mile = 5280 feet)

   • A. The mountain pass
   • B. The driveway
   • C. They have the same steepness
   • D. Cannot be determined

2. 2. Which is steeper: a truck ramp that rises 4 feet over a horizontal distance of 9 feet, or a toy truck ramp that rises 3 centimeters over a horizontal distance of 7 centimeters?

   • A. The truck ramp
   • B. The toy truck ramp
   • C. They have the same steepness
   • D. Cannot be determined

3. 3. The circumference, $C$, of a circle is recorded for two radii, $r$: for $r=4$, $C=25.133$, and for $r=10$, $C=62.832$. Calculate the rate of change $\frac{\Delta C}{\Delta r}$. Round to three decimal places. ___

4. 4. What is the slope of the line that passes through the points $(2, 4)$ and $(5, 13)$? The slope is ___.

5. 5. Find the slope of the line that contains the points $(-3, 7)$ and $(5, 3)$. Give your answer as a fraction. The slope is ___.

6. 6. The slope of a line is defined as the ratio of which two quantities?

   • A. The change in the x-coordinate to the change in the y-coordinate
   • B. The change in the y-coordinate to the change in the x-coordinate
   • C. The sum of the x-coordinates to the sum of the y-coordinates
   • D. The product of the coordinates

7. 7. A line passes through the points $(50, 25)$ and $(70, 85)$. Calculate the slope of the line. The slope is ___.

8. 8. What is the slope of any vertical line?

   • A. 0
   • B. 1
   • C. -1
   • D. Undefined

9. 9. Which line is decreasing: one with a slope of $\frac{1}{4}$ or one with a slope of $-2$?

   • A. The line with slope $\frac{1}{4}$
   • B. The line with slope $-2$
   • C. Both lines are decreasing
   • D. Neither line is decreasing