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

Question

x - time (minutes) 8 5 7 2 9
y - distance (meters) 40 25 35 10 45


(4 points)
Put responses in the correct input to answer the question.

a. Every minute [_] meters are traveled.

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

c. The relationship is [_] because the y-intercept is [_]

Answer 1

To find the answers to your questions, we can analyze the given data for time (x) and distance (y).

Given values:

• $x$ (time in minutes): 8, 5, 7, 2, 9
• $y$ (distance in meters): 40, 25, 35, 10, 45

a. Every minute [_] meters are traveled.

To find the average rate of distance traveled per minute, we can calculate the total distance traveled and divide it by the total time taken.

Total distance: $40+25+35+10+45=155$ meters

Total time: $8+5+7+2+9=31$ minutes

Average rate: $$\text{Average rate}=\frac{\text{Total distance}}{\text{Total time}}=\frac{155}{31}\approx 5\text{ meters per minute}$$

So, we can fill in the blank:

a. Every minute [5] meters are traveled.

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

To find the relationship between time (x) and distance (y), let's assume a linear relationship of the form:

$$y=mx+b$$

Where $m$ is the slope (distance per minute) and $b$ is the y-intercept.

From our calculation above, we found that the average distance per minute (slope $m$) is approximately 5. To find the y-intercept ($b$), we can choose a pair of data points; let's use the first point (8, 40).

Using the equation: $$y=mx+b$$ We can plug in $y=40$, $m=5$, and $x=8$:

$$40=5(8)+b40=40+bb=0$$

Thus, the relationship can be expressed as: $$y=5x+0\text{or simply}y=5x$$

So we fill in the blank:

b. Write an equation to show the relationship between x and y. [y = 5x]

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c. The relationship is [] because the y-intercept is [].

We have determined that the relationship is linear because we have established a linear equation in the format $y=mx+b$ with a constant slope.

Since $b$ (the y-intercept) is 0, we can fill in the blanks:

c. The relationship is [linear] because the y-intercept is [0].