Bell Work Problem: You have a 10 foot ladder leaning up against the side of the house. The ladder is sitting 5 feet from the base of the house. At what height does the ladder touch the house? Jill completed this problem as shown at the left. Did she set the problem up correctly? Is her answer correct? Justify your answers by showing work and explaining why Jill is or is not correct. (Hint: draw a diagram) Find the distance between the points (1, -3) and (9, 3) by using two different methods.

8.1 Representing Relationships Chapter 8 Lesson #1 Pg. 577

What You’ll Learn Linear equations can contain more than one variable A linear equation is an equation with a graph that is a straight line

Vocabulary Linear Equation Rate of Change Slope-Intercept Form An equation with a graph that is a straight line Rate of Change Change in the dependent variable divided by the change in the independent variable Slope-Intercept Form m = slope b = y-intercept Slope (m)

In a Table Remember….. If the change in the Domain (Independent Variable) is constant and the change in the Range (Dependent Variable) is constant you have a…. Linear Relationship Straight Line Graph

Writing Equations from a table Flow chart steps Find the “change in” both variables (Independent and Dependent) Calculate the Rate of Change (Slope) Substitute slope for the “m” in y = mx + b Use one coordinate value (x, y) from table and substitute for the x and y in Solve for “b” Write the equation in the form

Use the table at the left to solve the following example Write and equation to find the number of liters in any number of quarts. Then describe the relationship in words. Find change in variables Write equation and substitute in to find “b” Write equation and describe relationship Quarts, q Liters, l 1 0.95 2 1.9 3 2.85 4 3.8 5 4.75

Use equation to make a prediction How many liters are in 8 quarts?

Write equation and solve for “b” Use the graph at the left to write an equation to find the number of miles run (y) after any number of days (x) Find the slope Write equation and solve for “b” Write the equation of the line

Use equation to make a prediction How many miles will be run after 2 weeks?

Open Books to pg. 582 1a m = 50d + 0, he sends an average of 50 text messages per day. 1b 1500 messages

Multiple Representations m = 7w + 0 3b (table) 3c (graph) w 7w m 4 7(4) 28 5 7(5) 35 6 7(6) 42 7 7(7) 49

Homework Honors Pg. 583, 1 – 7 Regular Pg. 583, 1 – 5, 7