Question

Two points defining a linear function are shown in the table below. X у -18 – 14 -10 -12 What is the slope of the function?

Answer 1

The slope of the function is 2.

Step-by-step explanation:

In the given table, two points defining the linear function are provided with corresponding values of x and y. To determine the slope of the function, we can use the formula:

Slope(m)= Change in y/Change in x

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Selecting two points from the table, let's say (-18, 14) and (-10, -12), we calculate the change in y and change in x:

Change in y=−12−14=−26

Change in x=−10−(−18)=8

Now, substitute these values into the slope formula:

m= -26/8 =2

Therefore, the slope of the function is 2. This indicates that for every unit increase in x, the corresponding y value decreases by 2 units, establishing the linear relationship between the variables.

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Answer 2

The slope of the linear function defined by the points (-18, -14) and (-10, -12) is calculated using the formula (change in y) / (change in x) and results in a slope of 0.25.

Step-by-step explanation:

The student asked for the slope of the linear function defined by two points on a table. To find the slope of a linear function, one could use the formula for the slope, which is rise over run, or the change in y-values divided by the change in x-values (delta y / delta x).

Given the two points (-18, -14) and (-10, -12), we calculate the slope as follows:

First, calculate the change in y by subtracting the second y-value from the first y-value: -12 - (-14) = 2.

Then, calculate the change in x by subtracting the second x-value from the first x-value: -10 - (-18) = 8.

Now divide the change in y by the change in x to find the slope: 2/8 = 0.25.

Therefore, the slope of the linear function is 0.25.