Line Navigator Worksheet
Algebra 1 Linear Equations & Graphing
Line Navigator Worksheet
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Key Reference: Slope-Intercept Form: \(y = mx + b\)
Slope (\(m\)): \(\frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}\) \(y\)-intercept: \((0, b)\) where \(x = 0\) \(x\)-intercept: \((a, 0)\) where \(y = 0\)
Part 1: Slope-Intercept Form Equations
Identify key features, show algebra for the \(x\)-intercept, and graph.
1. Equation: \(y = \frac{2}{3}x - 2\) Points: ___ / 4
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) _____ \()\)
\(x\)-Intercept \((\) _____ \(, 0)\)
Algebraic Work: Find \(x\)-intercept by substituting \(y = 0\):
x y 4 -4 4 -4 Scale: 1 unit/grid
2. Equation: \(y = -2x + 4\) Points: ___ / 4
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) _____ \()\)
\(x\)-Intercept \((\) _____ \(, 0)\)
Algebraic Work: Find \(x\)-intercept by substituting \(y = 0\):
x y 4 -4 4 -4 Scale: 1 unit/grid
3. Equation: \(y = -\frac{3}{4}x - 3\) Points: ___ / 4
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) _____ \()\)
\(x\)-Intercept \((\) _____ \(, 0)\)
Algebraic Work: Find \(x\)-intercept by substituting \(y = 0\):
x y 4 -4 4 -4 Scale: 1 unit/grid
Line Navigator • Page 1 of 2 Turn page for Standard Form →
Algebra 1 Line Navigator Worksheet • Page 2
Student Name:
Key Reference: Standard Form: \(Ax + By = C\)
\(x\)-intercept: Set \(y = 0 \to Ax = C\) \(y\)-intercept: Set \(x = 0 \to By = C\) Slope: \(m = -\frac{A}{B}\) (or solve for \(y\))
Part 2: Standard Form Equations
Find intercepts algebraically, determine slope, and graph.
4. Equation: \(3x + 2y = 6\) Points: ___ / 4
Find \(x\)-int (set \(y=0\)):
Find \(y\)-int (set \(x=0\)):
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) ___ \()\)
\(x\)-Intercept \((\) ___ \(, 0)\)
x y 4 -4 4 -4 Scale: 1 unit/grid
5. Equation: \(x - 2y = 4\) Points: ___ / 4
Find \(x\)-int (set \(y=0\)):
Find \(y\)-int (set \(x=0\)):
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) ___ \()\)
\(x\)-Intercept \((\) ___ \(, 0)\)
x y 4 -4 4 -4 Scale: 1 unit/grid
6. Equation: \(2x + 3y = -6\) Points: ___ / 4
Find \(x\)-int (set \(y=0\)):
Find \(y\)-int (set \(x=0\)):
Slope (\(m\)) \(m =\) _____
\(y\)-Intercept \((0,\) ___ \()\)
\(x\)-Intercept \((\) ___ \(, 0)\)
x y 4 -4 4 -4 Scale: 1 unit/grid
Part 3: Reverse Engineer & Synthesis
Bonus Challenge
A mystery line has an \(x\)-intercept at \((4, 0)\) and a \(y\)-intercept at \((0, -2)\).
a) Find the Slope (\(m\)): \(m = \frac{y_2 - y_1}{x_2 - x_1} =\) ______
b) Slope-Intercept Form: \(y =\) ________________
c) Standard Form (\(Ax+By=C\)): ______________________
Line Navigator • Page 2 of 2 Total Points Possible: 28
Standard Launch Warm Up
Algebra 1 Bellringer 5–7 Minute Warm-Up
Standard Launch Warm Up
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Date:
Period:
Score:
Strategy Spotlight: Graphing \(Ax + By = C\) using Intercepts
\(x\)-int: Let \(y = 0 \to Ax = C\) \(y\)-int: Let \(x = 0 \to By = C\) Connect points with a line!
1. Graph the equation: \(2x + 4y = 8\) 3 pts
Step 1: Find \(x\)-intercept \((y = 0)\)
2x + 4(0) = 8
\(x\)-int: \((\) ______ \(, 0)\)
Step 2: Find \(y\)-intercept \((x = 0)\)
2(0) + 4y = 8
\(y\)-int: \((0,\) ______ \()\)
Use the intercepts to find the slope (\(m\)): \(m = \frac{\Delta y}{\Delta x} =\) _________
x y 4 -4 4 -4 Plot & Connect
2. Graph the equation: \(3x - 2y = 6\) 3 pts
Step 1: Find \(x\)-intercept \((y = 0)\)
3x - 2(0) = 6
\(x\)-int: \((\) ______ \(, 0)\)
Step 2: Find \(y\)-intercept \((x = 0)\)
3(0) - 2y = 6
\(y\)-int: \((0,\) ______ \()\)
Use the intercepts to find the slope (\(m\)): \(m = \frac{\Delta y}{\Delta x} =\) _________
x y 4 -4 4 -4 Plot & Connect
3. Error Analysis: Spot the Common Misconception 2 pts
Jordan was asked to find the intercepts of \(4x - 2y = 8\). Jordan wrote: “\(x\)-intercept is \((2, 0)\) and \(y\)-intercept is \((0, 4)\).”
What mistake did Jordan make?
What is the correct \(y\)-intercept?
Correct \(y\)-intercept: \((0,\) _____ \()\)
Standard Launch Warm Up • Algebra 1 Total Points: 8
