A graph titled Weight Loss Plan has weekly aerobic activity (hours) on the x-axis, and monthly weight loss (pounds) on the y-axis. A trend line goes through points (1.5, 2) and (3.5, 5).

Use the trend line for the data in the scatterplot to make a prediction. About how many pounds were lost per month with 4 hours of weekly aerobic activity?
3 pounds
4.5 pounds
6 pounds
7.5 pounds

1 answer

To make a prediction using the trend line information from the points (1.5, 2) and (3.5, 5), we first need to determine the equation of the line that passes through these points.

The two points given are:

  • Point 1: (1.5, 2)
  • Point 2: (3.5, 5)

To find the slope (m) of the line, we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{3.5 - 1.5} = \frac{3}{2} = 1.5 \]

Now that we know the slope, we can use one of the points to write the line's equation in point-slope form, which is \( y - y_1 = m(x - x_1) \).

Using point (1.5, 2):

\[ y - 2 = 1.5(x - 1.5) \] \[ y - 2 = 1.5x - 2.25 \] \[ y = 1.5x - 0.25 \]

Now, we can use this equation to make a prediction for \( x = 4 \) (4 hours of weekly aerobic activity):

\[ y = 1.5(4) - 0.25 \] \[ y = 6 - 0.25 \] \[ y = 5.75 \]

Now, rounding to the nearest logical option from the provided choices:

  • 3 pounds
  • 4.5 pounds
  • 6 pounds
  • 7.5 pounds

Since 5.75 pounds is closest to 6 pounds, the prediction for the monthly weight loss with 4 hours of weekly aerobic activity is:

6 pounds.