Graphing Using x and y
Intercepts in Standard Form
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
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
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)
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
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)
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)
X intercept: (5, 0)
Y intercept: (0, 3)
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
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:
Sugar Cookies
3 cups sugar
2 cups flour
½ tsp vanilla
1 tsp baking powder
1 tbsp nutmeg
Brownies
2 cups sugar
3 cups flour
½ tsp vanilla
1 tsp baking powder
1 tbsp nutmeg
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.
3x + 2y = 12
Brownies
Find the x and y intercepts. What do they mean
in the context of the situation?
Sugar Cookies
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
$1 Bills
5x + 1y = 40
$5 Bills
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.
Shirts
12x + 8y = 48
Pants
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.
4x + 3y = 60