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Quizzes > Mathematics

Steepest Slope Quiz: Which Linear Function Is Steepest?

Quick, free compare slopes quiz to check your algebra. Instant results.

Editorial: Review CompletedCreated By: Anuj ShahiUpdated Aug 28, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style graph with rising line and slope markings for slope quiz rise over run on golden yellow background

This quiz helps you find which linear function has the steepest slope by comparing graphs, tables, and points. Get instant results to see where to improve, then keep building skills with our slope-intercept form quiz, try graphing functions practice, or check your basics with a linear equation quiz.

What is the slope of the line passing through the points (2, 3) and (5, 7)?
4/3
3/4
-3/4
-4/3
The slope is calculated by (y2 - y1) / (x2 - x1) = (7 - 3)/(5 - 2) = 4/3. Slope measures the steepness of a line, showing rise over run. A positive value indicates the line rises from left to right. For more details see .
If a line has a rise of 5 units and a run of 2 units, what is its slope?
2/5
5/2
-5/2
0
Slope equals rise divided by run, so 5 ÷ 2 = 5/2. This ratio indicates how steep the line is. A positive slope means the line goes upward as x increases. Learn more at .
What is the slope of a horizontal line?
1
0
-1
Undefined
A horizontal line has no rise, only run, so its slope is 0. The change in y is zero while x changes. This means the line is perfectly flat. See .
What is the slope of a vertical line?
Undefined
0
-1
1
A vertical line has no run (?x = 0), making the slope division by zero, which is undefined. Vertical lines go straight up and down. For more, visit .
In the equation y = 2x + 1, what is the slope of the line?
-2
1
-1
2
In slope-intercept form y = mx + b, m represents the slope. Here m = 2, so the slope is 2. This indicates the line rises two units for every one unit it moves right. See .
Using the slope formula, what is the slope of the line through (1, 4) and (3, 8)?
1/2
-2
4
2
Slope = (8 - 4) / (3 - 1) = 4/2 = 2. The positive result means the line rises two units for each unit moved to the right. Check details at .
A line on a graph rises from left to right. Which description fits its slope?
Zero
Undefined
Negative
Positive
A rising line from left to right always has a positive slope because y increases as x increases. Negative slopes fall left to right. A zero slope is horizontal, and undefined applies to vertical lines. More info at .
Which of these equations has a slope of 3?
y = -3x + 5
y = 3x + 5
3y = x + 5
y = x/3 + 5
In y = mx + b form, m is the slope. For y = 3x + 5, m = 3, so the slope is 3. The others either have different coefficients or rearranged forms. Read more at .
Write the equation in slope-intercept form for the line through (2, -3) with slope 4.
y = -4x - 3
y = 4x - 5
y = 4x - 11
y = 4x + 5
Use y - y1 = m(x - x1): y + 3 = 4(x - 2), so y + 3 = 4x - 8 and y = 4x - 11. Slope-intercept form isolates y. See .
What is the slope of the line given by the equation 2x - 3y + 6 = 0?
3/2
-3/2
-2/3
2/3
Rearrange: -3y = -2x - 6 ? y = (2/3)x + 2. The coefficient of x is the slope, 2/3. Standard form ax + by + c = 0 gives slope -a/b. More at .
What is the relationship between the lines y = 2x + 3 and y = 2x - 4?
Coincident
Neither
Parallel
Perpendicular
Both lines have slope 2 but different intercepts, so they never intersect and are parallel. Parallel lines share the same slope. Review at .
Which equation represents a line perpendicular to y = 1/2x + 1 that passes through the origin?
y = -2x
y = -1/2x
y = 2x
y = 1/2x
Perpendicular slopes are negative reciprocals: -1/(1/2) = -2. Passing through (0,0) gives y = -2x. See .
Given the table of values, what is the slope? (1, 2), (2, 4), (3, 6)
2
3
1/2
-2
Pick any two points: slope = (4 - 2)/(2 - 1) = 2/1 = 2. The pattern continues linearly. More on interpreting tables at .
A line crosses the x-axis at (3, 0) and the y-axis at (0, -6). What is its slope?
2
-2
-1/2
1/2
Slope = (0 - (-6))/(3 - 0) = 6/3 = 2. The rise is from -6 to 0, and the run is 3. See axis intercept form at .
A car travels 100 miles in 2 hours assuming constant speed. What is the slope representing its speed in miles per hour?
100
50
0.02
2
Slope here is rise/run = distance/time = 100/2 = 50 miles per hour. Real-world slopes represent rates like speed. More examples at .
What is the slope of the line perpendicular to 3x + 4y = 12?
4/3
3/4
-3/4
-4/3
First convert: 4y = -3x + 12 ? y = -3/4x + 3, so slope is -3/4. The perpendicular slope is its negative reciprocal: 4/3. More at .
Write the equation in standard form of the line through (1, 2) and (-2, 4).
2x + 3y - 8 = 0
2x - 3y + 8 = 0
3x + 2y - 8 = 0
-2x + 3y - 8 = 0
Slope m = (4 - 2)/(-2 - 1) = -2/3. Using y - 2 = -2/3(x - 1) leads to 2x + 3y - 8 = 0. Standard form is ax + by + c = 0. See .
A tank holds 5 L after 2 minutes and 13 L after 5 minutes. What is the filling rate in liters per minute?
3/8
2/3
5/3
8/3
Rate = (13 - 5)/(5 - 2) = 8/3 L/min. This slope shows how fast volume changes over time. It's a real-world linear rate. More at .
What is the slope of a line parallel to 4x - 5y = 20?
4/5
5/4
-4/5
-5/4
Convert to y = mx + b: -5y = -4x + 20 ? y = (4/5)x - 4, so slope = 4/5. Parallel lines share the same slope. See .
A road climbs from 200 m to 1,500 m elevation over 10 km horizontal distance. What is the slope (rise/run)?
1.3
130
13
0.13
Rise = 1500 - 200 = 1300 m, run = 10 km = 10,000 m; slope = 1300/10000 = 0.13. This dimensionless ratio is the gradient. More at .
If a line has an x-intercept of 6 and a y-intercept of -2, what is its slope?
-3
3
-1/3
1/3
Intercept form: x/6 + y/(-2) = 1 ? y = -1/3 x + 2. The slope is -1/3. Intercepts give easy slope calculation. See .
Given f(x) = ax + b with f(1) = 2 and f(-1) = -4, what is the value of a (the slope)?
3
2
-2
-3
Set up: a(1)+b=2 and a(-1)+b=-4. Subtract: 2a=6 ? a=3. This solves simultaneous equations for slope. More at .
What is the slope of a line perpendicular to y = -1/5x + 7?
-1/5
-5
5
1/5
Original slope m = -1/5. The perpendicular slope is the negative reciprocal: -1/(-1/5) = 5. Perpendicular lines satisfy m1·m2 = -1. See .
What is the relationship between the lines 3x - 4y + 5 = 0 and 4x + 3y - 7 = 0?
Neither
Coincident
Parallel
Perpendicular
Convert each to y = mx + b. First gives m = 3/4, second gives m = -4/3. The product is -1, so they are perpendicular. Perpendicular criteria: slopes are negative reciprocals. See .
If a line y = mx + b is reflected across the x-axis, what is the slope of the reflected line?
1/m
-m
-1/m
m
Reflection across the x-axis changes y to -y, so the new equation becomes -y = mx + b ? y = -mx - b. The slope term is -m. Transformations of functions are covered at function transformations.
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Study Outcomes

  1. Calculate Slope with Rise over Run -

    Practice determining the slope of a line by computing rise over run in various calculate slope examples to build accuracy and speed.

  2. Apply Slope to Graph Linear Functions -

    Use slope values to plot and interpret linear functions, reinforcing skills from a comprehensive linear functions practice test.

  3. Interpret Slope in Context -

    Analyze real-world scenarios to understand how positive, negative, zero, and undefined slopes describe relationships between variables.

  4. Analyze Question Types in the Slope of a Line Quiz -

    Break down common problems from our slope of a line quiz to identify strategies for efficient problem solving.

  5. Compare Slope Scenarios in a Quick Slope Quiz -

    Differentiate among various slope cases through targeted comparisons, boosting your confidence in handling diverse line slopes.

  6. Utilize the Functions and Slope Quick Check Answer Key -

    Leverage the functions and slope quick check answer key to self-assess, pinpoint knowledge gaps, and direct focused review.

Cheat Sheet

  1. Slope Definition and Formula -

    Understanding slope starts with m = (y₂ - y₝) / (x₂ - x₝), famously remembered as "rise over run." This formula lets you quantify how steep a line is by comparing vertical change to horizontal change. Try a simple calculate slope example: between (2, 3) and (5, 9), m = (9 - 3)/(5 - 2) = 6/3 = 2.

  2. Positive, Negative, Zero, and Undefined Slopes -

    A positive slope rises left to right, while a negative slope falls, zero slope is perfectly horizontal, and an undefined slope is a vertical line. Recognizing these four cases is vital for interpreting graphs quickly and accurately. For instance, y = 4 has m = 0, while x = -2 is vertical with no defined slope.

  3. Calculating Slope from Two Points -

    Step through two-point slope problems by labeling (x₝, y₝) and (x₂, y₂), then apply the rise-over-run formula. Practice with diverse calculate slope examples to build confidence, such as finding m between (−1, 5) and (3, −1): m = (−1−5)/(3+1) = −6/4 = −3/2. Repetition on sample problems, like those on a linear functions practice test, solidifies your technique.

  4. Slope-Intercept and Point-Slope Forms -

    The slope-intercept form, y = mx + b, instantly reveals slope m and y-intercept b, making graphing a breeze. When you know one point (x₝, y₝) and m, switch to point-slope form: y − y₝ = m(x − x₝). Converting between these forms is a staple in any linear functions practice test.

  5. Real-World Applications of Slope -

    From calculating speed in physics (distance over time) to determining cost changes in economics, slope measures real change per unit. Visualizing slope in everyday contexts reinforces why linear functions matter and boosts confidence when tackling quick slope quiz questions. Remember: steepness always equals rate of change, whether in a mountain trail or a finance chart.

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