Number Line Lock Worksheet
Algebra 1 • Multi-Step Inequalities
Number Line Showdown
Name:
Date:
Period:
Score:
25
Which graph shows the solution to this inequality?
Standard Model
\(4w + 2(9w + 5) \le 6w - 6\)
A) -2 -1 0 1 2
B) -2 -1 0 1 2
C) -2 -1 0 1 2
D) -2 -1 0 1 2
Show algebraic steps below: Final Solution:
26
Which graph shows the solution to this inequality?
Standard Model
\(2m + 3(4m - 1) \le 6m + 5\)
A) -2 -1 0 1 2
B) -2 -1 0 1 2
C) -2 -1 0 1 2
D) -2 -1 0 1 2
Show algebraic steps below: Final Solution:
Standard Model Strategy: Distribute, combine like terms, isolate the variable, and plot the boundary point.
\(\le\) Ray Left • \(\ge\) Ray Right • Solid Dot Included
Keychain Fundraiser Graph Worksheet
Algebra 1 • Linear Models & Graphing
Keychain Fundraiser Graphing
Name:
Date:
Period:
Score:
The Student Council is selling custom keychains for a charity drive. A sponsor gave an initial donation of $40, and each keychain sold earns an additional $4.
Linear Model \(y = 4x + 40\)
First Quadrant Coordinate Plane Scale: Count by 5 on X-axis • Count by 10 on Y-axis
$0 $10 $20 $30 $40 $50 $60 $70 $80 $90 $100 $110 $120 $130 $140 0 5 10 15 20 25 Number of Keychains (\(x\)) Amount Raised (\(y\))
Part 1: Table of Values
Compute \(y = 4x + 40\) for each \(x\), then plot on the grid:
| Keychains (\(x\)) |
Rule: \(4x + 40\) |
Raised (\(y\)) |
\((x, y)\) |
| 0 |
\(4(0) + 40\) |
$40 |
\((0, 40)\) |
| 5 |
\(4(5) + 40\) |
|
|
| 10 |
\(4(10) + 40\) |
|
|
| 15 |
\(4(15) + 40\) |
|
|
| 20 |
\(4(20) + 40\) |
|
|
| 25 |
\(4(25) + 40\) |
|
|
Part 2: Graphing & Analysis
1. Plot each point from the table and draw a straight ray starting at \(x = 0\).
Check that all points line up with a straightedge.
2. Identify the \(y\)-intercept and describe what it means in context:
3. What is the slope, and what does it represent in dollars per keychain?
4. Use your graph to find the amount raised if 12 keychains are sold:
First Quadrant Note: Both \(x \ge 0\) and \(y \ge 0\) because keychains and dollars raised are non-negative real quantities.
X-Axis: Count by 5 • Y-Axis: Count by 10
