+Warm-Up Find the slope.

1)(4, -6) (4, 3)2)(5, 3) (-1, 8) 3)(1, 12) (-5, 12)

4)An employee’s wages are directly proportional to the time worked. If an employee earns $100 for 5 hours, How much will the employee earn is 18 hours?5)The amount of money that a magazine pays for an article varies directly as the number of words in the article. If the magazine pays $720 for a 1200-word article, how much will the magazine pay for a 1500-word article?6)When an electric current is 32 A (amperes), the electromotive force is 288 V (volts). Find the force when the current is 65 A, if the force varies directly as the current.

+

Graphing y=mx+bUnit 3 Day 2

http://www.youtube.com/watch?v=rBAGAdySKSQ

Rise up Run Out

Investigation

+Some of the best vacuum cleaners are only sold door-to-door. The salespeople demonstrate the cleaning ability of the appliance in people’s homes to encourage them to make the purchase. Michael sells vacuum cleaners door-to-door. He earns a base salary plus commission on each sale. His weekly earnings depend on the number of vacuum cleaners he sells as shown in the table below.

Number of Vacuum Cleaners Sold in a Week

2 4 6 8

Weekly Earnings (in Dollars) 600 960 1320 1680A. Identify the independent variable. Identify the dependent variable.B.  Write a NOW-NEXT rule to show how Michael’s weekly earnings E

can be calculated from the number of vacuum cleaners sold in week S.

C.  Find the rate of change in earnings as sales increase. D.  Write an equation in intercept form to show weekly earnings over

time. E. What part of Michael’s pay does this figure represent? What is the

meaning of the y-intercept? F. Use your equation to predict what the weekly earnings are for selling

15 vacuum cleaners G. Does Michael’s earnings appear to be a linear function of the

number of vacuum cleaners sold.

+Let’s wrap up what we found... What is the relationship between a...

NOW-NEXT equation: Next = Now + 5

Start = 20

And

Explicit equation:y = 5x + 20

+They mean the same thing! Except the explicit equation is a short cut!The explicit equation y=5x + 20 comes from the equation y=mx+b.

This has a special name:

Slope intercept form

Why do you think it has this name?

+Slope Intercept Form

y = mx+b

Slope

Y- Intercept

Using Slope and y-Intercept to Graph Linesy=mx+b

• Given a point on the line, you can use the slope to get to the "next" point by counting “rise over run".

But how do you find your first point?

• y = mx + b, "b" gives the y-intercept, and "m"

is the slope. We can use this fact to easily graph straight lines!

LET’S GRAPH! Y= -2/3x + 4 Y= 2x – 3

+You can represent linear relationships with a graph, a table of values, an equation, or a rule stated in words. Here are two relationships. Give all the other ways to show each relationship.

Day (x)

Height (in cm)

3 44 55 67 8

b) a)

Now Lets Write the equation! 1) Find m 2) Pick a point and plug in y, x, and m 3) Solve for b4) Rewrite

+Example 2 - Write the equation of the line for the following

b) (-1,2) and (4,5) a) Day (x)

Height (in cm)

5 97 119 13

+Your Turn – Write an equation of a line for the following. 1. (2, 4) and (5, 6) 2. M= -2 and b = 43. With a slope of 2 and

through the point (1,3) 4. (-3,5) and (-1, 6)

+3-2 Classwork y = mx + b Day 2 Classwork Due at the end of class

Graphing Worksheet Match the equations at the

back with the graphs! Homework if you do not

finish