Slope Checkpoint Exit Ticket
CP Algebra 1 Notes 4-2 • Day 1
Rate of Change & Slope Exit Ticket
Name:
Date:
Period:
Score: _____ / 6 pts
Goal: Find, interpret, and calculate rates of change and slopes of lines.
Show all steps. Simplify fractions.
1
Rate of Change from a Table (Real-World Context)
2 Points
The table shows the total cost \(y\) of buying gallons of gasoline \(x\) at a station.
| Gallons (\(x\)) |
Cost in $ (\(y\)) |
| 4 |
$14.00 |
| 7 |
$24.50 |
| 10 |
$35.00 |
Part A: Find the rate of change using any two points. \(\text{Rate} = \frac{\Delta y}{\Delta x}\)
Work:
Rate =
Part B: Explain the meaning in context (include units).
Meaning:
2
Constant Rate of Change (Linear or Non-Linear)
2 Points
Determine whether the table represents a linear function. If it is linear, state the constant rate of change.
Linear? YES NO
Show differences (\(\Delta y\) and \(\Delta x\)):
Constant Rate of Change (if linear): \(m =\)
Reasoning:
3
Slope of a Line from a Graph
2 Points
Find the slope of the line graphed below. Write your final answer in simplest form.
x y 2 4 -2 -4 2 4 -2 -4
Points on line: \((\) , \()\) and \((\) , \()\)
Vertical Change (\(\text{rise}\)) = Horizontal Change (\(\text{run}\)) =
Show fraction & simplification:
Final Slope (\(m\)):
\(m =\)
Self-Check: Rate your confidence on today's concepts:
1 (Need Help) 2 (Getting There) 3 (Got It) 4 (Mastered)
Slope Checkpoint Answer Key
Teacher Resource Notes 4-2 • Day 1
Rate of Change & Slope — Answer Key & Guide
Total: 6 Points
Mastery Threshold: 5 / 6 pts (83%)
Objective: Assess student ability to calculate, interpret, and represent rates of change and slopes from tables and graphs.
Formative Checkpoint
1
Question 1 Solution: Rate of Change from Table
2 Points Total
Part A (1 pt): Calculation Correct Value: $3.50/gal
Using points \((4, 14.00)\) and \((7, 24.50)\):
\(\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{24.50 - 14.00}{7 - 4} = \frac{10.50}{3} = \mathbf{3.50}\text{ \textbf{or} }\mathbf{\$3.50\text{ per gallon}}\)
Part B (1 pt): Real-World Meaning Must include units
Exemplar: "Gasoline costs $3.50 per gallon" or "For every additional 1 gallon of gas purchased, the total cost increases by $3.50."
Common Errors
- Inverting the ratio: \(\frac{\Delta x}{\Delta y} = \frac{3}{10.50} \approx 0.29\) (gallons per dollar).
- Missing units: Writing "3.5" without context or dollar sign.
Give 0.5 pt partial credit if calculation is correct but units are omitted.
2
Question 2 Solution: Constant Rate of Change
2 Points Total
Interval Checks & Decision (1 pt) Linear: YES [✓]
\(\Delta x = 0 - (-3) = +3\), \(3 - 0 = +3\), \(6 - 3 = +3\) (constant \(\Delta x = 3\))
\(\Delta y = 5 - 11 = -6\), \(-1 - 5 = -6\), \(-7 - (-1) = -6\) (constant \(\Delta y = -6\))
\(\frac{\Delta y}{\Delta x} = \frac{-6}{3} = \mathbf{-2}\) for every interval.
Rate & Reasoning (1 pt) m = -2
Reasoning: "Yes, it is linear because there is a constant rate of change of \(-2\) (\(y\) decreases by 6 each time \(x\) increases by 3)."
Common Errors
- Sign error: Stating \(m = +2\) by neglecting negative changes in \(y\).
- Single check: Checking only first pair without verifying all intervals.
Full credit requires both correct "YES", \(m = -2\), and verbal reasoning.
3
Question 3 Solution: Slope from Graphed Line
2 Points Total
Points & Rise / Run Breakdown (1 pt) Points: (-3, 4) & (1, -2)
Points identified: \((-3, 4)\) and \((1, -2)\) [or \((-1, 1)\)]
\(\text{Vertical Change (Rise)} = -6\) (line goes down 6 units)
\(\text{Horizontal Change (Run)} = +4\) (line goes right 4 units)
Final Slope (1 pt): \(m = \frac{-6}{4} = \mathbf{-\frac{3}{2}}\) (or \(\mathbf{-1.5}\))
m = -3/2
Common Errors
- Positive slope: Writing \(+\frac{3}{2}\) (ignoring negative direction).
- Inverted run/rise: Writing \(-\frac{2}{3}\) or \(-\frac{4}{6}\).
- Unsimplified: Writing \(-\frac{6}{4}\) (deduct 0.5 pt).
Accept \(m = -\frac{3}{2}\), \(-\frac{3}{2}\), or \(-1.5\).
Diagnostic Scoring & Day 2 Action Plan
Use scores to organize warm-up groups tomorrow
5 – 6 Points: Proficient
Ready for Day 2 formal slope formula \(m = \frac{y_2-y_1}{x_2-x_1}\) across all four quadrants and vertical/horizontal special cases.
3 – 4 Points: Target Review
Student typically struggles with negative signs on slopes or forgets units. Spend 5 mins on Day 2 warm-up reviewing directional signs.
0 – 2 Points: Intensive Reteach
Pull into small group during Day 2 practice. Re-anchor with "rise over run" color-coded triangles before calculating coordinate differences.
