Question

Which equation shows the linear relationship in the table? x −2 −1 0 1 2 y −34 −12 10 32 54 y = 10x + 22 y = 22x + 10 y = 22x − 10 y = 10x − 22

Answer 1

The correct linear equation that represents the relationship between x and y is y = 22x + 10, which is determined by calculating the slope using two data points and then finding the y-intercept.

Step-by-step explanation:

The question is asking to determine the linear equation that represents the relationship between the variables x and y based on a given data table. We can use the points provided in the table to determine the slope and y-intercept to form the equation of a line in the format y = mx + b, where m is the slope and b is the y-intercept.

To find the correct linear equation, we can calculate the slope by taking two points from the table, for instance (1, 32) and (2, 54), and applying the formula for slope: m = (y2 - y1) / (x2 - x1). Here, the slope m = (54 - 32) / (2 - 1) = 22. Next, we can use the slope and any point from the table to find the y-intercept b. Using the point (0, 10), we substitute the values into y = mx + b, yielding 10 = 22(0) + b, which simplifies to b = 10. Therefore, the linear equation that describes the relationship is y = 22x + 10.

Answer 2

The equation that shows the linear relationship in the table is y = 10x - 22.

Step-by-step explanation:

The table shows the values of x and y. To determine which equation represents the linear relationship, we need to find the equation that relates x and y in a linear manner. Let's examine the options:

Option A: y = 10x + 22

Option B: y = 22x + 10

Option C: y = 22x - 10

Option D: y = 10x - 22

We can substitute the x values from the table into each equation and see which equation matches the corresponding y values.

For example, if we substitute x = -2 into Option A, we get y = 10(-2) + 22 = 2, which does not match the corresponding y value of -34 in the table. If we continue this process for all the x values, we find that only Option D, y = 10x - 22, matches all the corresponding y values in the table. Therefore, Option D represents the linear relationship in the table.