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

Question

The table shows the relationship between the number of apples and the total weight of the basket. After 1 apple, the total weight of the basket is 8 ounces. After 3 apples, the total weight is 20 ounces. Plot the two points on the graph to show the total weight of the basket of apples after 1 apple and 3 apples are put in the basket.
Number of apples Total weight (oz)
1 8
3 20
Excellent!
For each apple 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 apples 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
(1, 8)(3, 20)
0
1
2
3
4
5
0
4
8
12
16
20
24
28
32
36
40
Number of apples
Total weight (oz)
y= mx + b

Slope =

Answer 1

To find the slope (m) of the line that represents the relationship between the number of apples (x) and the total weight (y), we can use the two points given: (1, 8) and (3, 20).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Using our points:

• \( (x_1, y_1) = (1, 8) \)
• \( (x_2, y_2) = (3, 20) \)

Now, substituting the values:

\[ m = \frac{20 - 8}{3 - 1} = \frac{12}{2} = 6 \]

So the slope \( m \) is \( 6 \).

Next, we can use the slope-intercept form of the linear equation \( y = mx + b \). We already have \( m = 6 \).

Now, we need to find the y-intercept \( b \). We can use one of the points to find \( b \). Let's use the point \( (1, 8) \):

\[ 8 = 6(1) + b \] \[ 8 = 6 + b \] \[ b = 8 - 6 = 2 \]

So, the equation of the line that represents the relationship between the number of apples and the total weight is:

\[ y = 6x + 2 \]

Final Answer:

• Slope \( m \): 6
• Equation: \( y = 6x + 2 \)

Points to Plot:

• For (1, 8)
• For (3, 20)

Graph

You can plot the points (1, 8) and (3, 20) on the graph with the x-axis as the number of apples and the y-axis as the total weight in ounces. Then, draw a straight line through the two points to represent the linear relationship.