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Korina is filling a basket with oranges of equal weight. Draw a graph and write an equation to represent this situation.

The table shows the relationship between the number of oranges and the total weight of the basket. After 2 oranges, the total weight of the basket is 15 ounces. After 5 oranges, the total weight is 27 ounces. Plot the two points on the graph to show the total weight of the basket of oranges after 2 oranges and 5 oranges are put in the basket.
Number of oranges Total weight (oz)
2 15
5 27
Nice!
For each orange added to the basket, the total weight increases at a constant rate. So, we can draw a line through these two points to show the linear relationship between the number of oranges and the total weight in ounces. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line?
x
y
(2, 15)(5, 27)
0
1
2
3
4
5
6
0
3
6
9
12
15
18
21
24
27
30
33
Number of oranges
Total weight (oz)
y= mx + b

Slope =
Excellent!
What does the slope of 4 represent in this situation?
x
y
(2, 15)(5, 27)
0
1
2
3
4
5
6
0
3
6
9
12
15
18
21
24
27
30
33
Number of oranges
Total weight (oz)
y= mx + b
Slope = 4

The weight of the basket increases 4 ounces for each orange.

The weight of the basket increases 2 ounces for every 4 oranges.

The initial weight of the basket is 4 ounces.

1 answer

To find the slope \( m \) of the line that represents the relationship between the number of oranges and the total weight of the basket, we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points given in your table:

\((2, 15)\) and \((5, 27)\),

we can substitute into the slope formula:

\[ m = \frac{27 - 15}{5 - 2} = \frac{12}{3} = 4 \]

So, the slope \( m \) is 4.

What Does the Slope of 4 Represent?

The slope of 4 indicates that the total weight of the basket increases by 4 ounces for each orange added. Therefore, the correct interpretation is:

The weight of the basket increases 4 ounces for each orange.

Now, to complete the equation of the line in the form \( y = mx + b \):

We know the slope \( m = 4 \). To find \( b \), the y-intercept, we can use one of the points. Let's use the point \((2, 15)\):

\[ 15 = 4(2) + b \] \[ 15 = 8 + b \] \[ b = 15 - 8 = 7 \]

Thus, the equation of the line is:

\[ y = 4x + 7 \]

Summary:

  1. The slope \( m \) is 4.
  2. The equation representing the scenario is \( y = 4x + 7 \).
  3. The slope means that for each orange added, the weight of the basket increases by 4 ounces.