Slope Quiz
Questions: 16 · 10 minutes
1. A table pairs x-values 0, 2, and 4 with y-values 5, 4, and 3. What slope does the table represent?
A slope of −2, treating the y-change as the denominator.
A slope of −1/2, because y falls by 1 whenever x rises by 2.
A slope of 2, using only the spacing between consecutive x-values.
A slope of 1/2, ignoring the downward direction of the change.
2. What is the slope of the line through the points (−1, 2) and (3, 10)?
The slope is 2 because the rise is 8 and the run is 4.
The slope is 8 because only the change in y is used.
The slope is 1/2 because the rise and run have been reversed.
The slope is −2 because the first x-coordinate is negative.
3. A line has equation y = (1/2)x + 4. What is the slope of a line perpendicular to it?
A perpendicular slope of 2, the ordinary reciprocal.
A perpendicular slope of −2, the negative reciprocal.
A perpendicular slope of −1/2, formed by changing only the sign.
A perpendicular slope of 1/2, matching the original line.
4. The points (1, 2) and (3, 6) lie on a line. Which additional point lies on that same line?
The point (4, 6), which keeps the second known y-value unchanged.
The point (5, 8), which increases both coordinates by 2.
The point (5, 10), which follows the line y = 2x.
The point (6, 10), which preserves a coordinate difference of 4.
5. Which equation represents the line through (2, 1) and (6, 9)?
y = 2x + 3, which has the correct slope but misses both points.
y = 2x − 3, which has slope 2 and passes through both points.
y = (1/2)x, which reverses the required slope.
y = 4x − 7, which uses the horizontal change as its slope.
6. A student tries to find the slope between (7, −2) and (7, 5). Why does the calculation not produce a defined slope?
The y-values have opposite signs, so no slope can be calculated.
The rise is 7, which is too large to form a slope.
The run is 0, and division by zero is undefined.
The two points must include the origin before slope can be found.
7. What does a positive slope indicate when a line is read from left to right?
Its vertical position stays constant as x increases.
Its y-values decrease as its x-values increase.
Its graph necessarily passes through the coordinate origin.
Its y-values increase as its x-values increase.
8. A path rises 6 meters over a horizontal run of 2 meters. What is its slope?
A slope of 1/3, found by dividing run by rise.
A slope of 3, found by dividing 6 meters by 2 meters.
A slope of 4, found by subtracting the run from the rise.
A slope of 8, found by adding the rise and run.
9. Which slope represents the steepest line when every graph uses the same scale on both axes?
−4, because its absolute value is the greatest.
3/2, because every positive slope is steeper than a negative one.
1/2, because smaller fractions indicate greater steepness.
Zero, because a horizontal line has the widest run.
10. A student calculates the slope between (1, 4) and (5, 12) as (4 − 12) ÷ (5 − 1) = −2. Which correction produces the actual slope?
Take the absolute value of every slope result, regardless of point order.
Divide the horizontal change by the vertical change to obtain 1/2.
Keep the subtraction order consistent: (12 − 4) ÷ (5 − 1) = 2.
Add the coordinate changes instead of dividing them to obtain 12.
11. Which line is parallel to y = 3x + 2?
y = 3x − 7, because it has the same slope and a different intercept.
y = (1/3)x − 7, because its slope is the reciprocal of 3.
y = 2x + 3, because the slope and intercept exchange values.
y = −3x + 2, because it keeps the same slope magnitude.
12. Which point-slope equation represents a line with slope −3 passing through (2, 5)?
y + 5 = −3(x + 2), which substitutes both coordinates with the wrong signs.
y − 2 = −3(x − 5), which reverses the x- and y-coordinates.
y − 5 = 3(x − 2), which uses the correct point but the opposite slope.
y − 5 = −3(x − 2), which correctly uses y − y₁ = m(x − x₁).
13. Which formula gives the slope between two points (x₁, y₁) and (x₂, y₂), provided x₂ is not equal to x₁?
Subtract each point’s x-coordinate from its y-coordinate, then divide the results.
Divide the change in x by the change in y: (x₂ − x₁) ÷ (y₂ − y₁).
Divide the sum of the y-coordinates by the sum of the x-coordinates.
Divide the change in y by the change in x: (y₂ − y₁) ÷ (x₂ − x₁).
14. A line moves from the point (−2, 5) to the point (1, −1). What is its slope?
A positive slope of 2, using 6 as the rise and 3 as the run.
A negative slope of 1/2, obtained by reversing the ratio.
A negative slope of 6, using only the vertical change.
A slope of −2, since the change in y is −6 and the change in x is 3.
15. A wheelchair ramp rises 3 feet over a horizontal run of 12 feet. What is the ramp’s slope?
The ramp’s slope is 1/4 after simplifying 3/12.
The ramp’s slope is 4 because the run was divided by the rise.
The ramp’s slope is 1/3 because the rise alone determines the denominator.
The ramp’s slope is 9 because the rise was subtracted from the run.
16. A horizontal line passes through (0, −4) and (6, −4). What is its slope?
The slope equals −4 because that is the shared y-coordinate.
The slope equals 1 because the line extends to the right.
The slope is 0 because y does not change.
The slope is undefined because both points have negative y-values.