1. Lesson 4.5 Graph Using Slope-Intercept Form
Essential Question: How do you graph linear equations given in slope-intercept form?

2. Before we start… Consider the graph
What is the slope and y-intercept of the graph?
What does the slope represent in the context of the problem? What does the y-intercept represent in the context of the problem?
How do you think you can graph a linear equation knowing only the slope and y-intercept?

3. Before we start… Make a table of values for the equation 𝑦=4𝑥+3
Plot the points and draw a line.
Use the graph to find the slope and the y-intercept.

4. What is slope-intercept form?
A linear equation of the form y = mx + b is written in slope-intercept form where m is the slope and b is the y-intercept of the equation’s graph.

7. An equation needs to be in slope-intercept form to identify the slope and y-intercept.
If an equation is in standard form and you want to identify the slope and y-intercept, you have to rewrite the equation by solving for y.

8. Identify the slope and y-intercept

9. Identify the slope and y-intercept

10. Identify the slope and y-intercept

11. Identify the slope and y-intercept

12. Identify the slope and y-intercept

13. How do I graph an equation in slope-intercept form?
Make sure the equation is in slope-intercept form
y = mx + b
Identify the y-intercept and plot it.
Identify the slope.
Use the slope to plot another point.
Draw a line through your points.

20. Graph 𝑦=−𝑥+7

21. Graph 𝑦= 1 4 𝑥−5

22. What is the equation of the line graphed below?

23. What is the equation of the line graphed below?

24. What is the equation of the line graphed below?

25. What is the equation of the line graphed below?

26. How does this apply to real-life?
In real-world problems that can be modeled by linear equations, the y-intercept is often an initial value, and the slope is a rate of change.

27. Jeff’s restaurant sells hamburgers
Jeff’s restaurant sells hamburgers. The amount charged for a hamburger, h, is based on the cost for a plain hamburger plus an additional charge for each topping, t, as shown in the equation below. ℎ=0.60𝑡+5 What does the number 0.60 represent in the equation? What does the number 5 represent in the equation?

28. Your favorite pizza restaurant charges you $8
Your favorite pizza restaurant charges you $8.95 for a large pizza with no toppings and an extra $0.75 for each topping you add to the pizza. The equation below represents that. 𝐶=0.75𝑡+8.95 What does the number 0.75 represent in the equation? What does the number 8.95 represent in the equation?

29. Escalators To get from one floor to another at a library you can take either the stairs or the escalator. You can climb stairs at a rate of 1.75 feet per second, and the escalator rises at a rate of 2 feet per second. You have to travel a vertical distance of 28 feet. The equations model the vertical distance d (in feet) you have left to travel after t seconds.
Stairs: 𝑑=−1.75𝑡+28 Escalator: 𝑑=−2𝑡+28
Graph the equations in the same coordinate plane.
How much time do you save by taking the escalator?

30. You can use a laser or inkjet printer to print an 18 page report
You can use a laser or inkjet printer to print an 18 page report. The laser printer prints 6 pages/min and the inkjet printer prints 4.5 pages/min. The models give the number of pages p left to print after t minutes.
Laser: 𝑝 = −6𝑡 + 18 Inkjet: 𝑝 = −4.5𝑡 + 18
Graph both models in the same coordinate plane.
How many minutes do you save using the laser printer?

31. a. Graph both equations in the same coordinate plane.
Television A company produced two 30 second commercials, one for $300,000 and the second for $400,000. Each airing of either commercial on a particular station costs $150,000. The cost C (in thousands of dollars) to produce the first commercial and air it n times is given by 𝐶=150𝑛+300. The cost to produce the second and air it n times is given by 𝐶=150𝑛+400.
a. Graph both equations in the same coordinate plane.
b. Based on the graphs, what is the difference of the costs to produce each commercial and air it 2 times? 4 times? What do you notice about the differences of the costs?

32. Graph both equations in the same coordinate plane.
A violin teacher charges a one-time sheet-music fee of $20 for adults and no fee for children. The charge per hour is $20 for both children and adults. The cost C for children for n lessons is given by C = 20n and for adults by C = 20n + 20.
Graph both equations in the same coordinate plane.
Based on the graphs, what is the difference in the costs?

33. What are parallel lines?
Two lines in the same plane are parallel if they do not intersect and have the same slope.
Remember slope gives the rate at which a line rises or falls.

34. Determine which of the lines are parallel

35. Determine which of the lines are parallel

36. Determine which of the lines are parallel a) 𝑦=3𝑥−5 b) 𝑦=7−3𝑥 c) −3𝑥+𝑦=8

37. Determine which of the lines are parallel a) 𝑦=− 2 3 𝑥+3 b) 𝑦=6+ 2 3 𝑥 c) 𝑦=1− 2 3 𝑥

38. Use slope and y-intercept
Graphing a Line
Standard Form?
Use x and y intercepts
Slope-Intercept Form?
Use slope and y-intercept
Not sure?
Use a table of values

39. How do you graph linear equations given in slope-intercept form?

40. Ticket Out the Door
Identify the slope and the y-intercept