Question

The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?

Answer 1

In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

What is the Y-intercept of a Linear equation?

A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.

Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:

Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)

Slope (m) = 2/1

Slope (m) = 2

To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b

3 = 1(2) + b

3 = 2 + b

Subtract 2 from both sides

3 - 2 = 2 + b - 2

1 = b

b = 1

Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

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