Question

what does the y-intercept of the line tell you about the situation? nick moves 1 yard farther from the goal line after each attempt. when he starts practicing, nick kicks the ball 5 yards from the goal line. after 15 attempts, nick kicks the ball 20 yards from the goal line. nick moves 5 yards farther from the goal line after each attempt.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a line in the form \(y = mx + b\) is the value of \(y\) when \(x = 0\). In the context of this graph, the x - axis represents the number of attempts and the y - axis represents the distance from the goal line. When \(x = 0\) (number of attempts is 0, meaning at the start of practicing), we look at the y - value.

Step2: Analyze the graph's y - intercept

From the graph, we can see that when \(x = 0\) (no attempts yet, start of practice), the y - value (distance) is 5. Now let's analyze each option:

• Option 1: This describes the slope (rate of change per attempt), not the y - intercept. So this is incorrect.
• Option 2: When \(x = 0\) (start of practicing), the distance is 5 yards. This matches the y - intercept interpretation.
• Option 3: This is a point on the line (\(x = 15,y = 20\)), not related to the y - intercept. So this is incorrect.
• Option 4: This also describes the slope (if it were true, the slope would be 5, but from the graph, the slope is \(\frac{15 - 5}{12-0}=\frac{10}{12}=\frac{5}{6}\approx0.83\) or other calculations show it's not 5), and it's about the rate, not the y - intercept. So this is incorrect.

Answer:

When he starts practicing, Nick kicks the ball 5 yards from the goal line.