Question

Which table represents a linear function? A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 2, 4, 8. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 3, 6. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 0, 1. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 3, 5, 7.

Answer 1

The table that represents a linear function is the last one: a two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 3, 5, 7.

This is because the second column has a constant rate of change (or slope) between any two consecutive values of x. The slope of the function can be calculated as:

slope = (change in y) / (change in x)

If we take any two consecutive values of x from the last table (e.g. x=0 and x=1), we can calculate the slope as:

slope = (y1 - y0) / (x1 - x0) = (3 - 1) / (1 - 0) = 2/1 = 2

If we do this for any other pair of consecutive values of x in the table, we will get the same slope of 2. This indicates that the function is a linear function with a constant slope of 2.

Answer 2

A linear function is a function that produces a straight line when it is graphed. The equation of a linear function is of the form y = mx + b, where m is the slope and b is the y-intercept.

Looking at the four tables, we can calculate the slopes of the lines that would be produced by each table. The slope is given by the change in y divided by the change in x.

For the first table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the second table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the third table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the fourth table, the change in y is 2, and the change in x is 1. Therefore, the slope is 2/1 = 2.

Only the first three tables have the same slope, which is 1. Therefore, only the first three tables represent a linear function.