2. Given the table for x, time in minutes and y, distance traveled in meters: x - time (minutes) 8 5 7 2 9 y - distance (meters) 40 25 35 10 45

Answer 1

To find the relationship between x (time) and y (distance), we can plot the data points on a graph.

The points (8, 40), (5, 25), (7, 35), (2, 10), and (9, 45) represent the time and distance pairs.

Plotting these points on a graph, we get:

(8, 40)
o
y
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| +
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| +
+ | +
o |
--------------------------------------------------- x
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2
| 5
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+---

The points roughly form a line, indicating a linear relationship between time (x) and distance (y).

The equation of a line can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Let's use the points (5, 25) and (7, 35) to find the slope:

m = (35 - 25) / (7 - 5)
m = 10 / 2
m = 5

So, the slope of the line is 5.

To find the y-intercept (b), we can use any of the points. Let's use (5, 25):

y = mx + b
25 = 5(5) + b
25 = 25 + b
b = 25 - 25
b = 0

Therefore, the equation that represents the relationship between time (x) and distance (y) is:

y = 5x + 0
y = 5x