Question

1. a baseball team scores the same number of runs in each of the first 4 innings. after that, the team did not score a run for the rest of the game, which lasts 9 innings. let x represent the innings of the game, and y represent the total number of runs.

part a
sketch the graph of this situation below.
graph with x-axis labeled innings (marked 4 and 9) and y-axis labeled total number of runs
part b
how would the graph change if the innings in which the team scores runs changes?

Explanation:

Step1: Analyze the first 4 innings

The team scores the same number of runs in each of the first 4 innings. Let's assume they score \( r \) runs per inning (we can think of \( r \) as a constant, say for simplicity \( r = 1 \) for visualization, but the key is the rate). So for \( x \) from 0 to 4 (innings), the total runs \( y \) will be \( y=rx \), which is a linear line with slope \( r \).

Step2: Analyze innings 5 - 9

After 4 innings, they don't score any runs for the remaining \( 9 - 4=5 \) innings. So for \( x \) from 4 to 9, the total runs \( y \) remains constant (equal to the runs at \( x = 4 \)). So the graph will be a line with positive slope from \( (0,0) \) to \( (4, 4r) \) (if \( r = 1 \), then \( (4,4) \)) and then a horizontal line from \( (4,4r) \) to \( (9,4r) \).

Step3: Sketch the graph

• Plot the x - axis as innings (from 0 to 9) and y - axis as total runs.
• Draw a line from the origin \( (0,0) \) with a slope (for example, if 1 run per inning, slope 1) to the point \( (4,4) \) (if \( r = 1 \)).
• Then draw a horizontal line from \( (4,4) \) to \( (9,4) \).

Answer:

The graph consists of two parts: a linear segment with a positive slope from \((0,0)\) to \((4, y_4)\) (where \(y_4\) is the total runs after 4 innings, e.g., \(y_4 = 4\) if 1 run per inning) and a horizontal segment from \((4, y_4)\) to \((9, y_4)\). For PART B, if the team scores runs in more innings, the horizontal segment (or the part where runs were constant) would be shorter or non - existent, and the linear part would extend further with the same slope, increasing the total runs at the end of 9 innings.