The data in the table illustrates a linear function. What is the slope of the linear function?
x| 0| 2|4|6
y|-5|-2|1|4
Please shoe me how to figure this out? Thank you.
when x increases by 2, y increases by 3. So, start with
y = 3/2 x
But y(0) would be 0, and the table says it is -5. So,
y = 3/2 x - 5
To find the slope of a linear function, you need to calculate the change in y divided by the change in x. In other words, you need to find the difference in y-values divided by the difference in x-values for any two points on the line.
Let's take the points (0, -5) and (2, -2) from the table.
The change in y is -2 - (-5) = -2 + 5 = 3.
The change in x is 2 - 0 = 2.
Now, we can find the slope by dividing the change in y by the change in x: 3/2.
Therefore, the slope of the linear function is 3/2.
To determine the slope of a linear function, you can use the formula:
slope = (change in y) / (change in x)
In this case, you have the following data points:
x: 0, 2, 4, 6
y: -5, -2, 1, 4
To find the change in y, subtract the y-values for the two points:
Change in y = y2 - y1
Let's calculate the change in y:
Change in y (between points 1 and 2) = -2 - (-5) = 3
Change in y (between points 2 and 3) = 1 - (-2) = 3
Change in y (between points 3 and 4) = 4 - 1 = 3
Next, find the change in x using the same method:
Change in x = x2 - x1
Calculating the change in x:
Change in x (between points 1 and 2) = 2 - 0 = 2
Change in x (between points 2 and 3) = 4 - 2 = 2
Change in x (between points 3 and 4) = 6 - 4 = 2
Now we can calculate the slope by dividing the change in y by the change in x:
Slope = (change in y) / (change in x)
Using any of the calculated change in y and change in x values, we get:
Slope = 3 / 2
Therefore, the slope of the linear function is 3/2.