โ ๏ธ Top Mistakes to Avoid on This Topic
- Swapping the subtraction order: Always do yโโyโ on top and xโโxโ on the bottom. Mixing this up changes the sign of your answer.
- Forgetting to simplify fractions: If m = 4/8, simplify to 1/2.
- Confusing zero slope with undefined slope: Horizontal = zero slope (y doesn't change). Vertical = undefined slope (x doesn't change).
- Using the wrong two rows in a table: Any two rows work โ but double-check your arithmetic!
Question 1 Easy
Find the slope of the line shown in Graph 1. (Line through (โ3, โ6) and (3, 6))
1
Pick two clear points from the graph: (โ3, โ6) and (3, 6)
2
m = (yโ โ yโ) รท (xโ โ xโ) = (6 โ (โ6)) รท (3 โ (โ3))
3
m = 12 รท 6 = 2
m = 2 (positive slope โ line rises from left to right)
Question 2 Easy
Find the slope of the horizontal line at y = 3.
1
Pick any two points on the line: (โ4, 3) and (4, 3)
2
m = (3 โ 3) รท (4 โ (โ4)) = 0 รท 8 = 0
3
A horizontal line ALWAYS has a slope of zero.
m = 0
Question 3 Easy
Find the slope of the line in Graph 3. (Line through (โ2, 6) and (6, โ2))
1
Points: (โ2, 6) and (6, โ2)
2
m = (โ2 โ 6) รท (6 โ (โ2)) = โ8 รท 8 = โ1
m = โ1 (negative slope โ line falls from left to right)
Question 4 Easy
Find the slope of the vertical line at x = 2.
1
Pick any two points on the line: (2, โ4) and (2, 4)
2
m = (4 โ (โ4)) รท (2 โ 2) = 8 รท 0
3
Division by zero is undefined. A vertical line ALWAYS has an undefined slope.
m = undefined
Question 5 Medium
Slope through (1, 4) and (5, 12)
1
(xโ, yโ) = (1, 4) (xโ, yโ) = (5, 12)
2
m = (12 โ 4) รท (5 โ 1) = 8 รท 4
3
m = 2
m = 2
Question 6 Medium
Slope through (โ2, 7) and (4, โ5)
1
(xโ, yโ) = (โ2, 7) (xโ, yโ) = (4, โ5)
2
m = (โ5 โ 7) รท (4 โ (โ2)) = โ12 รท 6
3
m = โ2
m = โ2
Question 7 Medium
Rate of change from Miku's recording table (x=minutes, y=bars recorded)
1
Choose any two rows: (0, 1) and (2, 7)
2
Rate = ฮy รท ฮx = (7 โ 1) รท (2 โ 0) = 6 รท 2 = 3
3
Verify with another pair: (4, 13) and (6, 19) โ (19โ13)รท(6โ4) = 6รท2 = 3 โ
Rate of change = 3 bars per minute
Question 8 Medium
Slope through (3, 1) and (6, 3)
1
m = (3 โ 1) รท (6 โ 3) = 2 รท 3
2
2 and 3 share no common factors โ already in lowest terms.
m = 2/3
Question 9 Hard
Len's balloon animal table (x=hours practised, y=animals per hour)
1
Choose rows (1, 8) and (3, 24): rate = (24โ8)รท(3โ1) = 16รท2 = 8
2
Verify: (5, 40) and (7, 56) โ (56โ40)รท(7โ5) = 16รท2 = 8 โ
3
Meaning: For every additional hour Len practises, he can make 8 more balloon animals per hour.
Rate of change = 8 balloon animals per hour, per hour of practice
Question 10 Hard
Slope through (โ2, 1/2) and (4, 7/2)
1
(xโ, yโ) = (โ2, 1/2) (xโ, yโ) = (4, 7/2)
2
yโ โ yโ = 7/2 โ 1/2 = 6/2 = 3
3
xโ โ xโ = 4 โ (โ2) = 6
4
m = 3 รท 6 = 1/2
m = 1/2
๐ค Stuck? Use These AI Prompts
Copy any of these into Claude or ChatGPT for instant help:
If you don't understand what slope means:"Explain what slope means in a linear equation to a 9th grader who is just learning it. Use a simple real-world example and explain the formula m = (yโโyโ)/(xโโxโ)."
If you got the wrong sign on your answer:"I am finding the slope through two points and I keep getting the sign wrong. Can you explain with an example why slope is negative when a line goes downhill and positive when it goes uphill?"
If you're confused about tables:"How do I find the rate of change from a table of x and y values? Show me an example with a table that has 4 rows and explain which values to subtract."
If you don't know the difference between zero and undefined slope:"What is the difference between a slope of zero and an undefined slope? Which one is horizontal and which is vertical? Draw me a description."
๐บ Learn More (search these on YouTube or Khan Academy)
- Khan Academy: Search "slope of a line Khan Academy" โ watch the "Intro to slope" and "Slope from two points" videos
- YouTube: Search "how to find slope Algebra 1" โ look for videos by The Organic Chemistry Tutor or Math with Mr. J
- Khan Academy: Search "rate of change from a table" for the table questions
- Practice quiz: On Khan Academy, search "slope" under Algebra 1 and try their interactive exercises for instant feedback