Do Now Graph the following points: - PowerPoint Presentation

Do Now Graph the following points: (4, 5) (-3, 2) (-6, 1) (0, -4)

Linear Functions Review

Key components of Lines y-intercept : the point where a line crosses the y-axis The y value will be 0 x-intercept: the point where a line crosses the x-axisThe x value will be 0slope:  

Ex 1 : Identify the x-intercept, y-intercept and slope of the graph of the linear function. Ex1

Identify the y-intercept, x-intercept and slope You do 1 :

Identify the y-intercept, x-intercept and slope You do 2 :

The Equation of a Line Slope – Intercept form of a Line: Point-slope form: m = slope b = y-intercept  

Find the equation of the line. Ex 1: m = 2 and b = 17 Ex2: m = and b = -5  

Find the equation of the line. You do 1 : m = - 2 and b = 1 You do 2 : m = and b = -4  

Find the equation of the line Ex 1

Find the equation of the line Ex 2 :

Find the equation of the line You do 1 :

Find the equation of the line You do 2 :

Homework Complete # 1-3, 4, 6, 8, 10, 12, 13-15 Algebra II-Section 1.3 Worksheet

Linear Data Sometimes the data in a chart will be linear. How can you tell it’s linear? Hours Studied0 1 1 2 3 4 Grade Earned 52 64 76 88 100 When we have data, the intercepts and slope have real life meanings. Y-intercept : grade earned with 0 study hours Slope : rate of change in an earned grade with resect to hours studied

Ex1 Finding the slope and y-intercept and equation(model) of linear data from a chart Hours Studied 0 1 1 2 3 4 Grade Earned 52 64 76 88 100 x = y = To Find Slope : To Find y-intercept To write the equation (model) using the information you found !

Ex1 Finding the slope and y-intercept and equation(model) of linear data from a chart Hours Studied 0 1 2 3 Grade Earned 52 64 76 88 Slope : Rate of Change: Y-intercept: Model:

Ex2 Find the slope, y-intercept and model for the data chart Months of growth 3 5 8 9 14 Length of hair (inches) 4 7 11.5 13 20.5 x = y = Slope : y-intercept : Rate of change (meaning of slope): Model:

You Do 1: Find the slope, y- intercept and equation(model) for the linear data Age of Car in Years 2 4 6 8 Value of Car $21,000 $15,000 $9,000 $3,000 x = y = Slope : y – intercept: Rate of change (meaning of slope): Model:

You Do 2 :Find the slope, describe the slope, find the y-intercept, describe its meaning and model the data Number of cars sold2 4 4 5 9 Total salary $30,000 $40,000 $45,000 $65,000 x = y = Slope = Rate of change: Y- intercept: Meaning of y- intercept:

Assigning Meaning to Parts of a Graph If real life data is represented by a graph, the intercepts and slope have meaning just like in a data chart. EX1 y -intercept: x-intercept:Slope and its meaning:Equation of line:

You Do 1 Find and assign meaning to the x-intercept, y-intercept and slope of the linear graph y-intercept slope Why would the x-intercept make no sense in this problem? Equation of lineLength is in inches and growth period is in weeks.

You Do 2 Find and assign meaning to the x-intercept, y-intercept and slope of the linear graph y-intercept x-intercept slope equation of line

Assigning Meaning to the Parts of a Linear Equation Ex 1: The equation y = 45x + 200 is a linear model of the total charge, y for a party at a restaurant with x people in attendance. What does the slope represent? What does the y-intercept represent? What does the x-intercept represent?

Ex 2: The equation h = - 3t + 48 represents a model of the height h , in inches, of water in a pool at time t in minutes. How can we determine the slope if we are not using x and y?What does the slope in represent?What does the y-intercept represent?What does the x-intercept represent?

You Do 1: The equation C = 240 + 25b is a linear model of the charge of a train ticket C if you bring b bags on the train. a) What does the slope represent?b) What does the y-intercept represent?c) Does the x-intercept make sense in this problem? Explain.You Do 2: The equation v = 320 – 10t is a linear model of the value v of a cell phone after t months.What does the slope represent?What does the y-intercept represent?c) Does the x-intercept make sense in this problem? Explain.

Linear Systems What is a system? Ex 1:Two prom venues charge a rental fee plus a fee per student. The table shows the total costs for different numbers of students at Lakeside Inn. The total cost y (in dollars) for x students at the Sunview Resort is represented by the equation y = 10x + 600. Lakeside InnNumber of students, xTotal cost, y 100 $1500 125 $1800 150 $2100 175 $2400 200 $2700 Which venue charges less per student? How many students must attend for the costs to be the same?

Understanding the Problem Which venue charges less per student ? How many students must attend for the costs to be the same?

You Do 1: The cost of parking in a parking garage in Chicago is represented by the equation y = 15x + 20 where y is the total cost (in dollars) and x is the time in hours. The table below shows the total cost to park in a parking garage in Denver. Which city’s parking garage charges more per hour? After how many hours would parking in both cities be the same? Hours, x 2 3 4 5 Cost, y 43 51 59 61

You Do 2: Kelly and Kim are both babysitters. Kelly charges a flat fee of $10 plus $6 per hour to babysit. The table below shows the hourly fee that Kim charges to babysit. number of hours, x Total fee, y 1 $22 2 $26 3 $30 4 $34 Who charges more per hour? How many hours must Kim and Kelly babysit for their charges to be the same?