Linear Essentials Warmup
Algebra 1 Bellringer 5–8 Minutes
Linear Essentials Warm-Up
Name:
Date:
Period:
1
Linear Graph & Intercepts
Multiple Choice
Identify the \(x\)-intercept and \(y\)-intercept of the linear function graphed below:
x y -4 -2 2 4 -2 2 4
A \(x\)-int: \((0, -4)\) | \(y\)-int: \((2, 0)\)
B \(x\)-int: \((-4, 0)\) | \(y\)-int: \((0, 2)\)
C \(x\)-int: \((4, 0)\) | \(y\)-int: \((0, -2)\)
D \(x\)-int: \((0, 2)\) | \(y\)-int: \((-4, 0)\)
2
Slope from Standard Form
Algebraic Steps
Find the slope (\(m\)) of the line represented by the standard form equation below:
\[ 3x - 4y = 12 \]
Show your work converting to \(y = mx + b\):
Slope (\(m\)):
\(y\)-intercept (\(b\)):
3
Linear Transformation
Conceptual Analysis
The parent function \( f(x) = x \) is transformed to create the function \( g(x) \):
\[ g(x) = -\frac{1}{2}x + 5 \]
Complete each statement describing the transformations:
A. Reflection / Direction: The negative sign reflects the graph across the:
\(x\)-axis \(y\)-axis
B. Steepness (Dilation): Compared to parent \(f(x)\), the line \(g(x)\) is:
Steeper Less steep (flatter)
C. Vertical Translation:
The graph shifts up / down by units.
4
Two Points: Multiple Select
Select TWO
A linear function passes through the two points:
\( (1, 7) \) and \( (5, -1) \)
Work area ↓
Select the TWO statements that are true about this function:
A. The slope of the line is \( m = -2 \).
B. The \(y\)-intercept is located at \( (0, 9) \).
C. The standard form equation is \( 2x - y = 9 \).
D. The line passes through the point \( (3, 5) \).
E. The graph rises from left to right as \( x \) increases.
Self-Assessment: 😊 Mastered 😐 Reviewing 🙁 Need Help Total Score: _____ / 4
