Question

question 6
1 pts
the table shows the linear relationship between the number of hours francis worked, x, and the amount of money francis earned, y. based on the table, how much did francis earn per hour?
francis’s earnings
number of hours worked | amount earned
1.25 | $17.50
3.75 | $52.50
5.5 | $77.00
options:
$17.50 per hour
$14.00 per hour
$35.00 per hour
$24.50 per hour

Explanation:

Step1: Recall the formula for slope (rate)

The rate (earnings per hour) in a linear relationship \( y = mx + b \) is the slope \( m \), calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are points from the table.
Take the first two points: \( (x_1,y_1)=(1.25, 17.50) \) and \( (x_2,y_2)=(3.75, 52.50) \).

Step2: Calculate the slope (earnings per hour)

Substitute into the slope formula: \( m=\frac{52.50 - 17.50}{3.75 - 1.25}=\frac{35}{2.5}=14 \).
We can verify with another pair, e.g., \( (3.75, 52.50) \) and \( (5.5, 77.00) \): \( m=\frac{77.00 - 52.50}{5.5 - 3.75}=\frac{24.5}{1.75}=14 \).

Answer:

\$14.00 per hour (corresponding to the option: B. \$14.00 per hour)