To represent the relationship between the number of oranges and the total weight of the basket, a linear equation can be written in the form y=mx+b. In this equation, m is the slope of the line, or the rate of change of the weight of the basket. We just solved for and interpreted the slope. Substitute the slope for m in our equation.

Question

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
y=
x+b

Slope = 4

Answer 1

To create the linear equation representing the relationship between the number of oranges (x) and the total weight of the basket (y), we can start from the given information.

You mentioned that the slope (m) is 4. The slope represents the increase in weight for each additional orange added to the basket.

Now, we also need to determine the equation in the form \( y = mx + b \), which includes the slope and the y-intercept (b). The y-intercept is the weight of the basket when no oranges are present (x = 0).

We have the points (2, 15) and (5, 27) to further help us find the y-intercept:

1. Use the slope-intercept form of the equation: \[ y = mx + b \] Given \( m = 4 \): \[ y = 4x + b \]

2. Substitute one of the points to find b. Let's use the point (2, 15): \[ 15 = 4(2) + b \] \[ 15 = 8 + b \] \[ b = 15 - 8 \] \[ b = 7 \]

3. Write the final equation: Substituting \( b = 7 \) into the equation gives: \[ y = 4x + 7 \]

Thus, the linear equation representing the relationship between the number of oranges and the total weight of the basket is:

\[ \boxed{y = 4x + 7} \]