Intercept Trail Worksheet
Algebra 1 • Linear Relationships
Name: Date: Period:
Intercept Trail: Two-Point Method
Determine the slope \(m\), then solve for the y-intercept \(b\) in \(y = mx + b\) using whole numbers.
Goal: Find \(b\) and coordinate \((0, b)\)
The 3-Step Strategy
1
Find the Slope (\(m\))
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
2
Substitute One Point \((x, y)\)
Plug \(m\) and one point into \(y = mx + b\)
3
Solve for \(b\) (Y-Intercept)
Isolate \(b\). The intercept is at \((0, b)\)
Model Problem: Given \((2, 7)\) and \((4, 13)\)
Step 1: Calculate slope \(m = \frac{13 - 7}{4 - 2} = \frac{6}{2} = 3\)
Step 2: Plug in \((2, 7)\) \(7 = 3(2) + b \implies 7 = 6 + b\)
Step 3: Solve for \(b\) \(b = 7 - 6 = 1\)
Y-Intercept: \(b = 1\) Coordinate: \((0, 1)\)
A Guided Practice • Show All 3 Steps
All slopes and y-intercepts are clean whole numbers
1. Line through \((1, 5)\) and \((3, 9)\)
Step 1: Calculate slope \(m\)
Step 2 & 3: Substitute \((x, y)\) and solve for \(b\)
\(m =\) \(b =\) Y-Intercept: (0, ____)
2. Line through \((2, 14)\) and \((5, 26)\)
Step 1: Calculate slope \(m\)
Step 2 & 3: Substitute \((x, y)\) and solve for \(b\)
\(m =\) \(b =\) Y-Intercept: (0, ____)
3. Line through \((3, 20)\) and \((7, 36)\)
Step 1: Calculate slope \(m\)
Step 2 & 3: Substitute \((x, y)\) and solve for \(b\)
\(m =\) \(b =\) Y-Intercept: (0, ____)
4. Line through \((2, 11)\) and \((6, 23)\)
Step 1: Calculate slope \(m\)
Step 2 & 3: Substitute \((x, y)\) and solve for \(b\)
\(m =\) \(b =\) Y-Intercept: (0, ____)
Checkpoint: Substitute the second point into your equation \(y = mx + b\) to verify your y-intercept! Page 1 of 2
Algebra 1 • Intercept Trail
Name:
Independent Practice & Applications
Show all work for full credit
B Calculate the Y-Intercept
Find \(m\), solve for \(b\), and write the coordinate
5. Points: \((1, 8)\) and \((4, 17)\)
\(m =\) \(b =\) Coord: (0, ___)
6. Points: \((3, 10)\) and \((5, 14)\)
\(m =\) \(b =\) Coord: (0, ___)
7. Points: \((4, 25)\) and \((6, 35)\)
\(m =\) \(b =\) Coord: (0, ___)
8. Points: \((2, 15)\) and \((8, 27)\)
\(m =\) \(b =\) Coord: (0, ___)
9. Points: \((1, 13)\) and \((5, 37)\)
\(m =\) \(b =\) Coord: (0, ___)
10. Points: \((3, 7)\) and \((7, 11)\)
\(m =\) \(b =\) Coord: (0, ___)
C Critical Thinking & Real-World Reasoning
11. Surveyor Error Analysis
Elena found the y-intercept for \((2, 11)\) and \((4, 17)\). She found \(m = 3\), then wrote:
\(11 = 3 + b \implies b = 8\)
Explain her error and find the correct \(b\):
Correct \(b =\) Coordinate: (0, ___)
12. Drone Altitude Mission
A drone ascends at a constant rate. At \(2\) seconds, it is \(14\) meters high: \((2, 14)\). At \(6\) seconds, it is \(30\) meters high: \((6, 30)\).
Find its climb rate and its starting launch height (the y-intercept, where time \(= 0\)).
Rate (\(m\)): m/s Launch Height (\(b\)): m
Remember: In context, the y-intercept represents the initial value when \(x = 0\). Page 2 of 2
