In a fitted line , the slope tells how the predicted output changes for one more unit of input. Graph the given equation in Desmos to check whether the line rises or falls, then use the axes to name the slope’s units. The constant is the prediction at zero input, not the rate.
Hints
- Hint 1
A slope is how much a line’s output changes when its input goes up by . In , look for the number multiplying . Which number plays that role here?
- Hint 2
The hat on means a prediction from the fitted line, not an athlete’s measured time. Read the negative sign as a direction: as training weeks increase, does the predicted time rise or fall?
Step-by-step
Read the slope of the fitted line
Step 1Check the line’s direction
The hat on means predicted time. Type in Desmos, using to graph that prediction. Desmos shows a line falling as you move right, so the predicted time falls as training weeks increase.
- Step 2
Find the slope in the equation
In , the slope is the predicted change in when goes up by . Here the coefficient of is , so that is the slope. The is instead the prediction when .
- Step 3
Give the slope its units and direction
The input counts weeks, and the predicted output counts seconds. So the slope gives the predicted change in seconds per additional week. Its negative sign means a decrease: for each additional week of training, the predicted 400-meter time decreases by seconds. Choice A.