1. Graphing Using x and y Intercepts in Standard Form

2. What is Standard Form???? We have worked with slope intercept form (y = mx +b) for a while now, but also need to be familiar with standard form Standard form: Ax + By = C You can rearrange your equation to be in either standard or slope intercept form

3. Finding the y intercept We have already looked at doing this from a graph, and in slope intercept form. The y intercept occurs when x = 0 To find the intercept in standard form, simply substitute x = 0 and solve for y

4. Finding the y intercept Example 3x + 5y = 15 – substitute x = 0 3(0) + 5y = 15 5y = 15 y = 3 The y intercept is (0, 3)

5. Finding the x intercept The x intercept occurs when y = 0 To find the intercept in standard form, simply substitute y = 0 and solve for x

6. Finding the x intercept Example 3x + 5y = 15 – substitute y = 0 3x + 5(0) = 15 3x = 15 x = 5 The x intercept is (5, 0)

7. Creating a Graph You can create a graph with just the intercepts For the equation: 3x + 5y = 15 we found that X intercept: (5, 0) Y intercept: (0, 3)

8. X intercept: (5, 0) Y intercept: (0, 3)

9. Why is this useful? The x and y intercepts are important parts of the equation because it tells us the value of the function at zero. Consider the following example

10. Bake Sale Mrs. Geyer is making two recipes for the bake sale: Sugar Cookies, and Brownies. The recipe for each makes 1 dozen cookies and is as follows: 3 cups sugar 2 cups flour ½ tsp vanilla 1 tsp baking powder 1 tbsp nutmeg 2 cups sugar 3 cups flour ½ tsp vanilla 1 tsp baking powder 1 tbsp nutmeg Sugar Cookies Brownies Let (x) represent the number of dozen sugar cookies, and (y) represent the number of dozen brownies made. If Mrs. Geyer used a total of 12 cups of sugar, write an equation for the situation showing all of the possible combinations she could have made cookies and brownies.

11. 3x + 2y = 12 Find the x and y intercepts. What do they mean in the context of the situation? Brownies Sugar Cookies

12. Lets Try Another Together Jim has $40 in his pocket. There is a mixture of $1 bills and $5 bills. Write an equation in standard form showing all of the possible combinations that he may have. Let (x) represent the number of $5 bills and (y) represent the number of $1 bills

13. 5x + 1y = 40 $1 Bills $5 Bills

14. With a Partner Mr. Swaner shops for his clothes at a discount store. Every pair of pants costs $12 and every shirt costs $8. He spent $48. Write an equation in standard form to show all of the possible combinations of items Mr. Swaner could have purchased. Let (x) represent the number of pants, and let (y) represent the number of shirts.

15. 12x + 8y = 48 Pants Shirts

16. One More The snack bar at a baseball game sells hamburgers for $4 and hot dogs for $3. During the game, the snack bar collected $60. Write an equation in standard form to represent the possible sales of hot dogs and hamburgers. Let (x) represent the number of hamburgers sold, and (y) represent the number of hotdogs sold.

17. 4x + 3y = 60