Slope Showdown Exit Ticket
Algebra 1 Lesson 4-2 • Rate of Change & Slope (Day 2)
Slope Showdown Exit Ticket
Score
______ / 10
Name:
Date:
Period:
Slope Formula Reminder:
\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}} \)
1 Slope Between Coordinates
3 Points
Find the slope of the line passing through the points \( (-3, 5) \) and \( (3, 1) \). Show all substitution steps and simplify your final answer completely.
Final Slope:
\( m = \)
2 Special Line Analysis
3 Points
Calculate the slope of the line passing through \( (5, -2) \) and \( (5, 6) \). Then determine whether the line is horizontal or vertical and explain how your calculation proves it.
Line Classification:
Slope is: _______________
Line is: ________________
Explanation / Reason:
3 Find the Missing Coordinate
4 Points
The line passing through the points \( (-3, 1) \) and \( (5, r) \) has a slope of \( m = \frac{3}{4} \). Set up an equation using the slope formula and solve for the value of \( r \).
Solved Value:
\( r = \)
Self-Check (Circle one):
1 - Need Help 2 - Almost There 3 - Confident 4 - Got It!
Teacher Note:
Slope Showdown Answer Key
Teacher Key Lesson 4-2 • Rate of Change & Slope (Day 2)
Slope Showdown Answer Key
Total Value
10 Points
Scoring Standard:
Award partial credit for correct formula setups even if minor arithmetic errors occur.
1 Slope Between Coordinates: \( (-3, 5) \) and \( (3, 1) \)
3 Points
Worked Solution:
\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{3 - (-3)} \) (+1 pt setup)
\( m = \frac{-4}{3 + 3} = \frac{-4}{6} \) (+1 pt signs/subtraction)
\( m = -\frac{2}{3} \) (+1 pt simplified fraction)
Common Errors:
- Subtracting negative: \( 3 - (-3) \neq 0 \).
- Inverting slope as \( \Delta x / \Delta y = -\frac{3}{2} \).
2 Special Line Analysis: \( (5, -2) \) and \( (5, 6) \)
3 Points
Worked Solution:
\( m = \frac{6 - (-2)}{5 - 5} = \frac{8}{0} \) (+1 pt calculation)
Classification: Slope is Undefined; Line is Vertical. (+1 pt)
Explanation: Division by zero is undefined. There is zero horizontal change (\( \Delta x = 0 \)), creating a vertical line \( x = 5 \). (+1 pt)
Key Distinction:
\( \frac{0}{\#} = 0 \) (Horizontal line).
\( \frac{\#}{0} = \text{Undefined} \) (Vertical line). Watch for students writing "slope = 0" instead of undefined.
3 Find Missing Coordinate: \( (-3, 1) \) and \( (5, r) \) with \( m = \frac{3}{4} \)
4 Points
Worked Solution:
\( \frac{r - 1}{5 - (-3)} = \frac{3}{4} \implies \frac{r - 1}{8} = \frac{3}{4} \) (+1 pt setup, +1 pt denominator)
\( 4(r - 1) = 3(8) \implies 4r - 4 = 24 \) (or multiply both sides by 8)
\( 4r = 28 \implies \) \( r = 7 \) (+1 pt solving, +1 pt correct value)
Common Errors:
- Forgetting distribution: \( 4(r - 1) = 4r - 1 \) instead of \( 4r - 4 \).
- Inverting ratio as \( \frac{8}{r-1} = \frac{3}{4} \).
Mastery Band (8–10 pts):
Ready for slope-intercept graphing & rate word problems.
Approaching (6–7 pts):
Provide targeted warmup on subtracting negatives and proportions.
Intervention (0–5 pts):
Pull for small-group reteach on formula order and zero vs. undefined.
