To find the slope \(m\) of the line that represents the relationship between the number of oranges \(x\) and the total weight \(y\), we can use the formula for slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points from the table:
- \( (x_1, y_1) = (2, 15) \)
- \( (x_2, y_2) = (5, 27) \)
Substituting in these values:
\[ m = \frac{27 - 15}{5 - 2} = \frac{12}{3} = 4 \]
The slope \(m = 4\) means that for each orange added to the basket, the total weight increases by 4 ounces.
Finding the y-intercept \(b\)
Now that we know \(m\), we can use one of the points to find the y-intercept \(b\) in the equation \(y = mx + b\). Let's use the point \( (2, 15) \):
\[ 15 = 4(2) + b \] \[ 15 = 8 + b \] \[ b = 15 - 8 = 7 \]
The equation
Now we can write the equation of the line:
\[ y = 4x + 7 \]
Graph
To illustrate this, we can graph the two points:
- Point \( (2, 15) \)
- Point \( (5, 27) \)
On the x-axis, label the number of oranges (0 to 6) and on the y-axis, label the total weight (0 to 33 ounces). Plot the points and draw a line through them:
- For \(2\) oranges, plot the point at \( (2, 15) \).
- For \(5\) oranges, plot the point at \( (5, 27) \).
- Draw a straight line through both points to represent the relationship.
The resulting graph would be a straight line with a positive slope, indicating that as the number of oranges increases, the total weight also increases linearly.