Page 2: Writing Linear Equations from Tables

This page focuses on the process of deriving linear equations from tabulated data.

Vocabulary:

• Slope formula: m = $y₂-y₁$/$x₂-x₁$
• Rate of change: The change in y divided by the change in x

Example: Using the table with points (0,5) and (2,7):

1. Calculate slope: m = $7-5$/$2-0$ = 1
2. Identify y-intercept: b = 5
3. Write equation: y = x + 5

Page 3: Practice Problems with Tables

This page provides multiple examples of writing equations from tables with clear step-by-step solutions.

Highlight: Key steps for finding equations from tables:

1. Calculate slope using consecutive points
2. Identify y-intercept from x = 0 value
3. Combine in slope-intercept form

Example: For a table showing points (0,4), (1,7), (2,10):

• Slope = $7-4$/$1-0$ = 3
• Y-intercept = 4
• Equation: y = 3x + 4

Page 4: Advanced Table Analysis

This page covers scenarios where the y-intercept isn't directly given in the table.

Definition: When the y-intercept isn't in the table, use point-slope form first, then convert to slope-intercept form.

Example: For points (2,8) and (4,13):

1. Find slope: m = $13-8$/$4-2$ = 2.5
2. Use point-slope form: y - 8 = 2.5$x - 2$
3. Solve for y-intercept

Page 5: Real-World Applications

This page demonstrates how to write equations for real-world scenarios using tables.

Example: The automatic pet feeder problem:

• Initial amount: 24 cups
• Rate of decrease: -3 cups per meal
• Equation: f$n$ = -3n + 24

Highlight: In real-world problems:

• Slope represents rate of change
• Y-intercept represents initial value

Page 6: Real-World Context and Terminology

This page focuses on identifying slope and y-intercept in word problems.

Vocabulary:

• Rate of change keywords: "per," "every," "each"
• Y-intercept keywords: "initial value," "starting amount," "membership fee"

Example: "There is already 3 inches of snow on the ground, and it is snowing at a rate of 1.5 inches per hour."

• Slope $m$ = 1.5 (rate of snowfall)
• Y-intercept $b$ = 3 (initial snow)
• Equation: y = 1.5x + 3

Context and Variables

This section focuses on identifying variables and components in word problems.

Vocabulary: Independent variable (input) and dependent variable (output) help structure equation writing.

Example: In the dancing club scenario, monthly fee represents slope and startup fee represents y-intercept.

Practical Applications

The final content pages show how to apply linear equations to everyday situations.

Example: Rose's hourly wage problem demonstrates how salary depends on hours worked.

Highlight: Real-world scenarios help connect abstract concepts to practical applications.

Page 1: Writing Equations from Graphs

This page introduces the fundamental concepts of writing linear equations from graphs in slope-intercept form.

Definition: Slope-intercept form is written as y = mx + b, where m represents the slope and b represents the y-intercept.

Highlight: To write an equation from a graph:

1. Identify the slope using rise over run
2. Locate the y-intercept where the line crosses the y-axis
3. Substitute these values into y = mx + b

Example: For a line with slope 3 and y-intercept -6, the equation would be y = 3x - 6