The graph shows how many apples Erin can pick if she maintains a constant rate. What is the linear equation for this relationship?

Question

How many apples can she pick per hour? Drag numbers to complete the statements.
Numbers may be used once, more than once, or not at all.

Graph of a diagonal line on a coordinate plane going up and to the right with Time (h) on x-axis and Number of apples on y-axis. When h is 0, Number of apples is 0. When h is 1, Number of apples is 75
50 added to
0125075100
y =
75
x
Erin can pick
50
apples per hour.

Answer 1

To analyze the information in the problem, we need to establish a linear equation based on the graph and given points.

From the details:

• When \( h = 0 \) (0 hours), the number of apples \( y = 0 \).
• When \( h = 1 \) (1 hour), the number of apples \( y = 75 \).

The slope of the line (change in \( y \) over the change in \( x \)) indicates how many apples Erin can pick per hour.

The slope (m) is calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{75 - 0}{1 - 0} = \frac{75}{1} = 75 \]

This means Erin can pick 75 apples per hour.

Using the slope and the point \( (0, 0) \) to write the linear equation, we can use the slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept (which is 0 in this case).

The equation representing the relationship is: \[ y = 75x \]

In conclusion:

• The linear equation is \( y = 75x \).
• Erin can pick 75 apples per hour.

To fill in the completion statements:

• y = 75x
• Erin can pick 75 apples per hour.