The data in the table illustrate a linear function.

x –3 0 3 6
y –5 –3 –1 1
What is the slope of the linear function? Which graph represents the data?

slope = ∆y/∆x

so, for the first two points, the slope is 2/3
to be sure, check other point pairs

To find the slope of a linear function, we can use the formula:

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

Let's calculate the change in y and change in x using the given data:

change in y = (y2 - y1) = (-3 - (-5)) = 2
change in x = (x2 - x1) = (0 - (-3)) = 3

Now, we can substitute these values into the slope formula:

slope = (change in y) / (change in x) = 2/3

Therefore, the slope of the linear function is 2/3.

To determine which graph represents the data, we can plot the points on a graph and look for a pattern. Let's plot the points (x, y):

(-3, -5)
(0, -3)
(3, -1)
(6, 1)

Looking at the graph, we can see that the points form a straight line. Based on the given data and the slope calculated, the graph that represents the data would be a linear graph with a positive slope, rising from left to right.

Please note that I cannot physically show you the graph as I am an AI text-based bot, but I hope this information helps you visualize it.

To determine the slope of a linear function, you need to find the change in y (vertical change) divided by the change in x (horizontal change) between any two points on the line. Let's choose two points: (-3, -5) and (6, 1) from the given data table.

The change in y is: 1 - (-5) = 1 + 5 = 6.
The change in x is: 6 - (-3) = 6 + 3 = 9.

Therefore, the slope of the linear function is: 6/9 = 2/3.

Now, to determine which graph represents the given data, we will look at the slope-intercept form of a linear function, which is y = mx + b, where m is the slope and b is the y-intercept.

Using the slope we just calculated (2/3) and inspecting the given data, we notice that the y-intercept is -3 when x is 0. Therefore, the equation for the linear function in slope-intercept form is y = (2/3)x - 3.

Now, let's check the given graphs and determine which one matches the equation we derived. Plot the points (-3, -5), (0, -3), (3, -1), and (6, 1) on each graph and look for the graph where they all lie on the same line.

Once you identify the graph where all the points lie on the plotted line, that graph represents the given data.