To determine the slope \( m \) of the line that represents the total weight of the basket as a function of the number of pears, we can use the formula for the slope between two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \( (x_1, y_1) = (1, 12) \)
- \( (x_2, y_2) = (4, 39) \)
Now, substituting the coordinates into the slope formula:
\[ m = \frac{39 - 12}{4 - 1} = \frac{27}{3} = 9 \]
So the slope \( m = 9 \). This indicates that for each pear added, the total weight increases by 9 ounces.
Next, we can use one of the points to find the y-intercept \( b \). We'll use the point \( (1, 12) \) and the equation of a line in the form \( y = mx + b \).
Substituting \( x = 1 \), \( y = 12 \), and \( m = 9 \):
\[ 12 = 9(1) + b \]
This simplifies to:
\[ 12 = 9 + b \]
To solve for \( b \):
\[ b = 12 - 9 = 3 \]
So the y-intercept \( b = 3 \). Now we can write the equation that represents the relationship between the number of pears \( x \) and the total weight \( y \):
\[ y = 9x + 3 \]
Summary:
- Slope (m): 9
- Y-Intercept (b): 3
- Equation: \( y = 9x + 3 \)
Graph:
To plot the graph:
- Mark the points \( (1, 12) \) and \( (4, 39) \).
- Draw a line through these points, extending in both directions. The line will have a steep positive slope.
Let me know if you need any further assistance!