Linear Forms Intercepts Worksheet
Algebra 1 • Practice TEKS A.12E (Literal Equations)
Linear Forms & Key Intercepts
Page 1: Transforming Equations • Standard Form & Slope-Intercept Form
Name:
Date:
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Part 1: Transform Linear Equations (TEKS A.12E) Show all inverse operations and algebraic steps
Problem 1: Standard Form Rewrite to \( Ax + By = C \)
\( A \ge 0 \) (integers)
1a \( y = -7x + 3 \) Standard Form
Standard Form:
1b \( y = -4x + 9 \) Standard Form
Standard Form:
Problem 2: Slope-Intercept Form Rewrite to \( y = mx + b \)
Isolate \( y \)
2a \( 3x + 2y = 6 \) Slope-Intercept
Slope-Intercept:
2b \( 5x + 2y = 10 \) Slope-Intercept
Slope-Intercept:
Key Reminder Standard Form: \( Ax + By = C \) with \( A \ge 0 \). Slope-Intercept Form: \( y = mx + b \) with slope \( m \) and \( y \)-intercept \( b \).
Page 1 of 2 → Turn over for Graphs
Algebra 1 • Practice TEKS AR.3A & A.3C (Key Attributes)
Linear Forms & Key Intercepts
Page 2: Analyzing Coordinate Graphs • Slope Direction & Intercept Identification
Graph Analysis Section
Part 2: Identify Intercepts from Graphs (TEKS AR.3A / A.3C) Determine slope type & write ordered pairs for all intercepts
Problem 3: Graph A Linear Function
x y -4 -2 2 4 4 2 -2 -4
Slope Type:
Positive Negative
\(x\)-intercept: Where line crosses \(x\)-axis
( , )
\(y\)-intercept: Where line crosses \(y\)-axis
( , )
Problem 4: Graph B Linear Function
x y -4 -2 2 4 4 2 -2 -4
Slope Type:
Positive Negative
\(x\)-intercept: Where line crosses \(x\)-axis
( , )
\(y\)-intercept: Where line crosses \(y\)-axis
( , )
Attribute Comparison Check:
Graph A Observation:
As \(x\) increases, \(y\) decreases (falls from left to right). The \(y\)-intercept is positive, and the \(x\)-intercept is positive.
Graph B Observation:
As \(x\) increases, \(y\) increases (rises from left to right). The \(y\)-intercept is negative, and the \(x\)-intercept is positive.
Key Concept The \(x\)-intercept is the point \( (x, 0) \). The \(y\)-intercept is the point \( (0, y) \).
Page 2 of 2
Linear Forms Intercepts Answer Key
Teacher Answer Key Algebra 1
Linear Forms & Key Intercepts
Page 1 Solutions: Transforming Equations • Standard Form & Slope-Intercept Form
Key: Instructor Reference
Subject: Algebra 1
Score: 100%
Part 1 Solutions: Transform Linear Equations (TEKS A.12E) Complete algebraic steps & inverse operations shown
Problem 1: Standard Form Rewrite to \( Ax + By = C \)
\( A \ge 0 \)
1a \( y = -7x + 3 \) Solved
Given: \( y = -7x + 3 \)
Add \( 7x \) to both sides: \( +7x \quad +7x \)
Result: \( 7x + y = 3 \)
\( A = 7, B = 1, C = 3 \) (Integers, \( A \ge 0 \))
Standard Form: \( 7x + y = 3 \)
1b \( y = -4x + 9 \) Solved
Given: \( y = -4x + 9 \)
Add \( 4x \) to both sides: \( +4x \quad +4x \)
Result: \( 4x + y = 9 \)
\( A = 4, B = 1, C = 9 \) (Integers, \( A \ge 0 \))
Standard Form: \( 4x + y = 9 \)
Problem 2: Slope-Intercept Form Rewrite to \( y = mx + b \)
Isolate \( y \)
2a \( 3x + 2y = 6 \) Solved
Subtract \( 3x \): \( 2y = -3x + 6 \)
Divide each by \( 2 \): \( \frac{2y}{2} = \frac{-3x}{2} + \frac{6}{2} \)
Slope-Intercept: \( y = -\frac{3}{2}x + 3 \)
Slope \( m = -\frac{3}{2} \), \( y \)-intercept \( b = 3 \)
Slope-Intercept: \( y = -\frac{3}{2}x + 3 \)
2b \( 5x + 2y = 10 \) Solved
Subtract \( 5x \): \( 2y = -5x + 10 \)
Divide each by \( 2 \): \( \frac{2y}{2} = \frac{-5x}{2} + \frac{10}{2} \)
Slope-Intercept: \( y = -\frac{5}{2}x + 5 \)
Slope \( m = -\frac{5}{2} \), \( y \)-intercept \( b = 5 \)
Slope-Intercept: \( y = -\frac{5}{2}x + 5 \)
Teaching Note Check that students divided both terms by the leading coefficient when isolating \( y \).
Answer Key • Page 1 of 2
Teacher Answer Key Algebra 1
Linear Forms & Key Intercepts
Page 2 Solutions: Analyzing Coordinate Graphs • Annotated Intercepts
Annotated Graph Key
Part 2 Solutions: Graph Intercepts & Attributes (TEKS AR.3A / A.3C) Intercepts highlighted with coordinates on each coordinate plane
Problem 3: Graph A Solution Solved Key
x y -4 -2 2 4 4 2 -2 -4 (0, 2) (4, 0)
Slope Type:
Positive ✓ Negative (Falling)
\(x\)-intercept: Crosses \(x\)-axis at \(x = 4\)
( 4 , 0 )
\(y\)-intercept: Crosses \(y\)-axis at \(y = 2\)
