Graphing: Slope-Intercept Form A cab ride has an initial fee of $5.00 plus $0.20 for every mile driven. Let s define the variables and write a function that represents this situation. We can complete the following table to help us graph the function:!! 0 10 20 30 Why are there no negative!-values in our table?
Graph the points from our table on the coordinate plane. What is the slope of the graph? This is the rate of change. What is the!-intercept of the graph? This is the initial cost of the cab ride. What do you notice about the slope and y-intercept that you found from the graph and the numbers in your function?
This equation format is called slope-intercept form.! =!" +! We can use the slope-intercept form to help us efficiently graph a linear function! Let s look at the equation,! = 2! + 4 What is the slope of the function? What is the!-intercept of the function? Once we know the slope and!-intercept, we can now graph the function!
Let s Practice Graph the following equation! =!!! + 3.
Graphing: Standard Form We ve seen equations that look like this:! =!!! 3 That is an equation written in slope-intercept form. Another way to write the same equation is 3! 4! = 12. This is standard form.!" +!" =!. How does 3! 4! = 12 look different from its slope-intercept form of an equation,! =!!! 3?
What is the!-intercept of the graph? What is the!-intercept of the graph? What do you notice about the intercepts of our graph and the values from the standard form of the equation? Standard form allows us to easily find the intercepts and use these points to graph the function!
Let s go back to the standard form of the equation: 3! 4! = 12 First, let s find the!-intercept of the equation. For any!-intercept, what is the value of!? Now, let s find the!-intercept of the equation. For any!-intercept, what is the value of!?
Now that we have both intercepts, we can plot these points on a graph. We can verify our graph is correct by plotting a few more points.
Let s Practice Graph the following equation. 2! + 3! = 6
Graphing: Real-World Context Shaunte likes to take her children to the local art museum on the weekends. The museum charges an initial fee of $4.00 and then $1.50 for each time they visit. Define the variables and write a function to model this situation. Let s graph our function below:
What is the!-intercept? What does it represent? What is the slope? What does it represent? Why is only the first quadrant graphed for this situation?
Let s Practice The local fair charges $2.00 to enter plus $0.50 for every ticket purchased to ride the rides. Graph the function that represents this situation below: What is the!-intercept? What does it represent? What is the slope? What does it represent?
Determining the Equation of a Graph Consider the graph below. What is the!-intercept of this graph? What is the slope of this graph? How can we use this information to write a function that represents this graph?
Let s Practice Find the equation of the graph below.
Interpreting Real-World Context of Slope and Y-Intercept Kristen is tracking the weight gain of her new Great Dane puppy, one of the largest breeds of dogs in the world. The puppy s weight gain is represented by the function! = 5! + 3 where! represents the total weight of the puppy and! represents the age of the puppy in weeks. What is the slope of the function? What does the slope represent in this situation? What is the!-intercept of the function? What does the!-intercept represent in this situation?
Let s Practice A climber is scaling a steep mountain. His ascent is represented by the function! = 330h + 400, where! is the total height, in feet, of the climber and h is the number of hours that the climber has been climbing. Which of the following statements is true? A. The slope is the initial height of the climber, 400 feet, and the!-intercept is the distance that he climbs per hour, 330 feet. B. The total height of the climber is 730 feet. C. The slope is the distance that the climber ascends per hour, 330 feet, and the!-intercept is the initial height of the climber, 400 feet. D. The slope is the number of hours that the climber ascended and the!-intercept is the initial height of the climber, 400 feet.