Ready to master how to find slope from two given points? In this free scored quiz, you'll test your skills at calculating rise over run, tackle zero, undefined, and standard slopes, and see how quickly you can find the slope with two given points. Whether you're just starting with finding the slope given 2 points or aiming to calculate slope from two points under pressure, this challenge is your ticket to confidence. By the end, you'll know the slope formula inside out, boost your confidence for upcoming exams, and master tricky cases effortlessly. Explore the find slope of the line passing through the points tutorial if you need a refresher, then jump into our fun slope quiz and start proving your linear prowess - dive in now!
Find the slope of the line through the points (1, 2) and (4, 2).
1
0
2
A horizontal line has no change in y, so the rise is zero while the run is nonzero. Using the slope formula (y2 - y1)/(x2 - x1) gives (2 - 2)/(4 - 1) = 0/3 = 0. Therefore, the slope is zero. Learn more about horizontal slopes.
Find the slope of the line through the points (3, 5) and (3, -2).
0
-1
1
A vertical line has no change in x, so the run is zero and the slope is undefined. Plugging into (y2 - y1)/(x2 - x1) yields (-2 - 5)/(3 - 3) = -7/0, which is undefined. Vertical slopes are not real numbers. Read about vertical slopes here.
Find the slope of the line through the points (0, 0) and (2, 4).
-1
2
1/2
-2
Compute the rise and run: rise = 4 - 0 = 4, run = 2 - 0 = 2. Then slope = rise/run = 4/2 = 2. This line is steeper than a 45° angle line. See Khan Academy's slope guide.
Find the slope of the line through the points (1, -1) and (3, 1).
-1
2
0
1
Using the slope formula gives (1 - (-1))/(3 - 1) = 2/2 = 1. A slope of 1 means the line rises equally for each unit it moves right. This is the standard 45° diagonal. More on slope fundamentals.
Find the slope of the line through the points (-1, -1) and (-3, -3).
1
2
-1
-2
Here, rise = (-3) - (-1) = -2 and run = (-3) - (-1) = -2, so slope = (-2)/(-2) = 1. Both numerator and denominator are negative, giving a positive slope. Review slope calculations.
Find the slope of the line through the points (2, 5) and (5, -1).
1/3
3
-2
-6
Calculate rise = -1 - 5 = -6 and run = 5 - 2 = 3, so slope = -6/3 = -2. A negative slope means the line falls as you move right. Understand negative slopes.
Find the slope of the line through the points (-1, 4) and (3, 8).
1/2
1
2
-1
Here rise = 8 - 4 = 4 and run = 3 - (-1) = 4 so slope = 4/4 = 1. A slope of 1 indicates a 45° upward line. Learn more.
Find the slope of the line through the points (0, 7) and (4, 3).
-1
-4
1
0
Compute rise = 3 - 7 = -4 and run = 4 - 0 = 4, giving slope = -4/4 = -1. A slope of -1 shows a 45° downward line. Explore slopes further.
Find the slope of the line through the points (1, 2) and (3, 5).
1
2
1.5
3
The rise is 5 - 2 = 3, and the run is 3 - 1 = 2, so slope = 3/2 = 1.5. This shows the line rises 1.5 units for each unit right. See examples.
Find the slope of the line through the points (2, 3) and (5, 11).
4/3
8/3
2
3/8
Rise = 11 - 3 = 8, run = 5 - 2 = 3, so slope = 8/3. Fractions describe the exact steepness. Fractional slopes explained.
Find the slope of the line through the points (-3, 2) and (4, -5).
-7
-1
1
7
Rise = -5 - 2 = -7, run = 4 - (-3) = 7, so slope = -7/7 = -1. Watching sign changes is key. Review sign rules.
Find the slope of the line through the points (-2, 6) and (3, -4).
2
-2
-10
10
Rise = -4 - 6 = -10, run = 3 - (-2) = 5, so slope = -10/5 = -2. Large drops yield steep negative slopes. Negative slope details.
Find the slope of the line through the points (1.5, 2.5) and (4.5, 6.5).
3/2
2/3
4/3
3/4
Compute rise = 6.5 - 2.5 = 4 and run = 4.5 - 1.5 = 3, so slope = 4/3. Working with decimals is the same as with integers. Decimal slope examples.
Find the slope of the line through the points (-1, -1) and (4, 2).
5/3
-3/5
3/5
-5/3
Rise = 2 - (-1) = 3, run = 4 - (-1) = 5, so slope = 3/5. Fractional slopes less than 1 are gentler lines. Learn about fractional gradients.
Find the slope of the line through the points (3, 1) and (-2, 7).
6/5
-1
5/6
-6/5
Rise = 7 - 1 = 6, run = -2 - 3 = -5, so slope = 6/(-5) = -6/5. Negative fractions can be simplified but the sign remains. Check negative fractional slopes.
What is the slope of the line through the points (2, 5) and (5, 2)?
3
-1
-3
1
Calculate (2 - 5)/(5 - 2) = -3/3 = -1. Notice that swapping x and y coordinates in the points gives a slope of -1. This pattern holds for any points of the form (a, b) and (b, a). See special point patterns.
What is the slope of a line perpendicular to the line passing through (1, 2) and (4, 6)?
3/4
-4/3
4/3
-3/4
First find the original slope: (6 - 2)/(4 - 1) = 4/3. A perpendicular line has the negative reciprocal, which is -3/4. This ensures the lines meet at a right angle. Perpendicular slope rules.
0
{"name":"Find the slope of the line through the points (1, 2) and (4, 2).", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Find the slope of the line through the points (1, 2) and (4, 2)., Find the slope of the line through the points (3, 5) and (3, -2)., Find the slope of the line through the points (0, 0) and (2, 4).","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}
Score5/17
Easy1/5
Medium2/5
Hard1/5
Expert1/2
AI Study Notes
Email these to me
You can bookmark this page to review your notes in future, or fill out the email box below to email them to yourself.
Study Outcomes
Understand how to find slope from two given points -
Derive and explain the rise-over-run formula to compute slope between any two coordinates, reinforcing the conceptual meaning of slope as a rate of change.
Calculate slope from two points -
Apply the slope formula to determine a line's slope using any pair of coordinates, ensuring accurate computation for standard scenarios.
Identify zero and undefined slopes -
Distinguish horizontal and vertical lines by recognizing when the slope equals zero or is undefined, and understand the implications for graph behavior.
Interpret slope sign and magnitude -
Analyze how positive, negative, and fractional slopes affect a line's direction and steepness, enhancing your ability to read and sketch graphs.
Apply slope calculation across contexts -
Solve practice problems to find the slope with two given points from diverse coordinate sets, reinforcing problem-solving skills in varied scenarios.
Self-assess slope mastery -
Complete the free scored quiz to evaluate your proficiency in finding the slope given 2 points, identify areas for improvement, and boost your math confidence.
Cheat Sheet
Slope Formula Fundamentals -
The slope formula m = (y2 - y1)/(x2 - x1) calculates the steepness of a line connecting two points. This formula, commonly taught in university algebra courses and on sites like Khan Academy, applies universally whether coordinates are integers or fractions.
Identifying Zero Slope (Horizontal Lines) -
If y2 = y1, the numerator of (y2 - y1) equals zero, giving a slope of 0 and indicating a perfectly horizontal line. For example, between (1,3) and (5,3), m = (3-3)/(5-1) = 0, as noted in resources from MathisFun and MIT OpenCourseWare.
Recognizing Undefined Slope (Vertical Lines) -
When x2 = x1, the denominator (x2 - x1) becomes zero, making the slope undefined and signalling a vertical line. For instance, between (4,1) and (4,5), the division by zero reflects an infinite slope, a concept covered in Stanford's introductory algebra materials.
Applying Point-Slope and Slope-Intercept Forms -
Once you find the slope m, plug it into the point-slope form y - y1 = m(x - x1) and then rearrange to slope-intercept form y = mx + b for graphing or solving. This technique, highlighted in numerous curricula including University of California Berkeley's Pre-College Programs, bridges raw slope calculations with equation writing.
Mnemonics and Practice Strategies -
Use the "Rise Over Run" mnemonic or the acronym ROAR to remember that slope is the vertical change (rise) divided by the horizontal change (run). Consistent practice with diverse point pairs - tracked on platforms like IXL and Khan Academy - sharpens your ability to calculate slope quickly and accurately.
