Do Now Graph the equation by finding the intercepts. -5x + 7y = 35 Graph the equation by using a table. y = −2x + 1

Direct Variation Lesson 3-4

Rafael has a job selling electronics at Best Buy Rafael has a job selling electronics at Best Buy. He makes $9 an hour at his job. a. How much money will Rafael make if he works 0 hours? How many hours will Rafael have to work to make $700? b. Create a table to show how much money Rafael will make if he works 4, 8, and 12 hours. c. Graph the values from your table in part b. c. What is the slope of the line you graphed in part c?

Direct Variation A direct variation is described by an equation of the form y = kx, where k ≠ 0. This equation y = kx illustrates a constant rate of change where k is the constant of variation. The constant of variation can also be called the constant of proportionality.

Name the constant of variation for each equation Name the constant of variation for each equation. Then find the slope between the two points.

Direct Variation The constant of variation is always the same thing as the slope of the graph. The x- and y-intercepts of a direct variation graph are always (0, 0). To graph a direct variation graph, plot the point (0, 0) and use the slope to find the next point. Then connect the two points with a line.

Graphing Direct Variation Graph y = −6x. Graph y = 2x

Graphing Direct Variation Graph y = 4x. Graph y = 1 3 x

Writing a Direct Variation Equation If the relationship between the values x and y can be described by a direct variation equation, then we say that y varies directly as x. If y varies directly as x, then y = kx and we can solve for k. Once we have our direct variation equation, we can find any solutions to the equation.

Mr. Lightfoot’s example Suppose y varies directly as x, and y = 72 when x = 8. a. Write a direct variation equation that relates x and y. b. Use the direct variation equation to find x when y = 63.

On your own example Suppose y varies directly as x, and y = 98 when x = 14. a. Write a direct variation equation that relates x and y. b. Use the direct variation equation to find y when x = −4.

Independent Practice Grab one of the worksheets at the front of the room. Complete all of the problems and turn it in at the front of the room when you are finished. If you do not attempt the word problems, then you will get a zero for the assignment.