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
To find the slope of the linear function, we can use the formula:
slope = (change in y) / (change in x)
Let's pick two points from the table and find the slope:
slope = (y2 - y1) / (x2 - x1)
Using points (-3, -5) and (0, -3):
slope = (-3 - (-5)) / (0 - (-3)) = 2/3
Using points (0, -3) and (3, -1):
slope = (-1 - (-3)) / (3 - 0) = 2/3
Using points (3, -1) and (6, 1):
slope = (1 - (-1)) / (6 - 3) = 2/3
As we can see, the slope is constant and equal to 2/3. Therefore, the linear function can be written as:
y = (2/3)x - 3
To determine which graph represents the data, we can plot the points (-3, -5), (0, -3), (3, -1), and (6, 1) on the coordinate plane and connect them with a straight line with slope 2/3. The graph that matches the line passing through these points is the correct one.
To find the slope of a linear function, we can use the formula:
slope = (change in y) / (change in x)
Let's calculate the changes in y and x first:
Change in y = y2 - y1
= (-3) - (-5)
= 2
Change in x = x2 - x1
= 0 - (-3)
= 3
Now, we can calculate the slope:
slope = (change in y) / (change in x)
= 2 / 3
So, the slope of the linear function is 2/3.
To determine which graph represents the data, we can plot the points (x, y) from the table on each graph and see which one matches.