Question

Enter an equation relating the variables in the table. Express any value(s) in your answer as simplified fractions, if necessary.

6
15
21
27
Time (x)
Distance (y)
4
10
14
18
The equation is y =

Answer 1

A linear equation representing the relationship between Time (x) and Distance (y) in the table is y = (2/3)x. This equation was deduced using two points from the table to calculate the slope and then solving for the y-intercept using one of the points.

Step-by-step explanation:

Given the data in the table with Time (x) and Distance (y), we can determine the relationship between these two variables by finding a linear equation of the form y = mx + b where m is the slope and b is the y-intercept. To find the slope (m), we can take two points from the table and use the formula (y2 - y1) / (x2 - x1). Choosing the first two points (6, 4) and (15, 10), the slope is (10 - 4) / (15 - 6) = 6/9 = 2/3. The y-intercept (b) can be found by plugging in a value of x into the equation and solving for y. Since the equation must pass through every point in the table, we can choose any point to determine b. Using the point (6, 4), assuming our slope of 2/3:

y = (2/3)x + b
4 = (2/3)*6 + b
4 = 4 + b
b = 0

Thus, the equation relating Time (x) and Distance (y) is y = (2/3)x.