Numbers and Operations

Chapter 1

Numbers and Operations

Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Functions

1. Identifies situations in which one quantity changes at a constant rate per unit interval relative to another

A linear model describes situations where the dependent variable changes by the same amount for every equal step in the independent variable. This constant rate of change means the first differences in the table of values are always equal.

Equation form: y = mx + b

• m represents the constant rate of change (slope).
• b represents the initial or starting value (y-intercept).

The graph of a linear function is always a straight line. If the slope is positive, the line rises to the right; if negative, the line falls to the right.

Examples:

• A plumber charges a $50 service fee plus$25 per hour. Function: C(h) = 25h + 50. Each additional hour adds the same cost.
• A car rental is $40 per day. Function: R(d) = 40d. Each day increases the total cost by the same amount.
• Water flows into a tank at 5 liters per minute. Function: V(t) = 5t. Each minute increases volume by 5 liters.