Given the table for x, time in minutes and y, distance traveled:

x - time 4 3 10 7 9
y - distance 76 57 190 133 171


(4 points)

a. Every minute (Response area) meters are traveled.

b. Write an equation to show the relationship between x and y. (Response area)

c. This relationship is (Response area) because the y-intercept is (Response area) .

options for the "response area" blanks, (4, 76), 19, proportional, y = 133x, y = 19x, (0, 57), y = x = 19, non proportional, y x/19, (0, 19), 76, 19y, = x, -19, (0, 0), 57, 133

1 answer

Let's answer each part based on the given data.

a. Every minute ___ meters are traveled.

To find the average distance traveled per minute, we can calculate the slope (rate of change) based on the distance and time. We need to find \(y/x\) for each pair of values and see if it is consistent.

  • For x = 4, y = 76: \( \frac{76}{4} = 19 \)
  • For x = 3, y = 57: \( \frac{57}{3} = 19 \)
  • For x = 10, y = 190: \( \frac{190}{10} = 19 \)
  • For x = 7, y = 133: \( \frac{133}{7} \approx 19 \)
  • For x = 9, y = 171: \( \frac{171}{9} \approx 19 \)

Thus, every minute 19 meters are traveled.

b. Write an equation to show the relationship between x and y.

Since the distance per minute is constant (19 meters), we can express the relationship between x (time in minutes) and y (distance traveled) with a linear equation. The equation can be written as:

\[ y = 19x \]

c. This relationship is ___ because the y-intercept is ___.

The relationship is proportional because the line goes through the origin (0, 0) and there is a constant rate of distance traveled per unit of time.

The y-intercept is (0, 0) since when there is no time (x = 0), the distance traveled (y) is also 0.

Final Answers:

a. Every minute 19 meters are traveled.

b. Write an equation to show the relationship between x and y: y = 19x.

c. This relationship is proportional because the y-intercept is (0, 0).