1. Pre-Algebra Q3W2: Graphing Linear Equations and interpreting Graphs

2. Objective I can determine the “Initial Value” and rate of change of a function from a description of the relationship.

3. In the real world when something changes at a constant rate, it can be represented by a linear model. Example: Interpreting Graphs

4. Graphs must have an x- and a y-axis, and each axis must be labeled. “Time” goes on the x-axis. Example: Sam drives 3 miles per hour. How many hours does he drive in 3 hours? ____________ Rate of Change = ___________ Elements of a Graph

5. Review of Slope-Intercept Form Slope Intercept form is the equation of a line: y = mx + b m = slope b = y-intercept

6. Putting an Equation in Slope Intercept Form y = -2 + 3x can be written as: y = 3x -2: Slope: 3 y-Int: -2 What is the slope and y-intercept of: y = 5 – 4x: Slope: y-Int:

7. Identify the Slope and the y-Intercept Y = -7x + 2 Y = 5x – 6 Y = 8 – 9x Y = -2 + 10x Slope: -7; y-Int: 2 Slope: y-Int:

8. y = 2x + 1 Graphing Linear Equations

9. This graph represents the number of lawns Sam can mow in a given # of hours. How many lawns does he mow per hour? Interpreting Graphs

10. Sheryl works in an office where she prints a lot of worksheets. The printer starts with 20 sheets of paper, and she prints 20 sheets per day. Graph how many sheets of paper is in the printer on each day. (Note: “units” always go on your x axis. Units are frequently measures of time, like days, minutes, hours.) Creating Graphs from Real Life Situations

11. The “initial value” is the starting point. It is where x = 0. In other words, it is the y-intercept. Note in the last example, the initial value is 20: the printer started with 20 pages. Definition: Initial Value

12. The “initial value” is where x = 0. Let’s interpret what the initial value means in this example. Initial Value

13. What is the Initial Value? INITIAL VALUE = Y-INTERCEPT

14. What is the “Initial Value”?

16. James has $3 in the bank when he starts his new job. He earns $2/hour making toys for tots.: y = 2x + 3 What is the “Initial Value?” __________

17. Let’s Graph it Let’s Graph it: y = 2x + 3

18. Identify the Initial Value Equation y = 4x + 9 y = -x – 3 y = 8 + 4x y = -2 + 8x Initial Value 9