Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
5. Standard Form
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Exercise 40 Page 326

Write an equation to model the situation and then find its intersection points to graph it.

Practice makes perfect

We have the following information

  • Pineapple has 3 grams of carbohydrates per ounce.
  • Watermelon has 2 grams of carbohydrates per ounce.

We are preparing a fruit salad and we want the total carbohydrates from pineapple and watermelon to equal 24 grams. How can we show this combination with a graph? Well, let's make a plan!

Write an Equation

The equation should give us the total amount of carbohydrates equal to 24 grams. Let x be the weight of pineapple and y be the weight of watermelon in ounces. We can use this information to write an equation. 3x+ 2y= 24

Domain and Range of the Equation

In order to find reasonable domain and range, let's start with finding the intersection points of the equation. We can find the x-intercept by substituting 0 with y into the equation.

3x+2y=24
3x+2( 0)=24
3x=24
x=8

The x-intercept is 8. We can find the y-intercept in the same way.

3x+2y=24
3( 0)+2y=24
2y=24
y=12

We have found that the y-intercept is equal to 12. Since the minimum amount of pineapple and watermelon we can use is 0 grams, the domain and range will begin with zero grams and end with the intercepts. Domain:&[0,8] Range:&[0,12] Finally, let's graph the equation by plotting the intersection points and then connecting them.