Write the equation that represents the data in the table shown. Explain your answer.
x -6 -1 0 3 5
y -26 -6 -2 10 18
I am so confused on this. What do I do?
To find the equation that represents the relationship between the variables x and y, we can start by examining the difference between consecutive x-values and the corresponding y-values. Let's calculate the differences:
x: -6, -1, 0, 3, 5
y: -26, -6, -2, 10, 18
Difference in x-values: 5 - (-6) = 11
Difference in y-values: 18 - (-26) = 44
From the differences, we can see that there is a constant difference between consecutive x-values and y-values. This suggests that the relationship between x and y is linear.
Next, we can find the slope (m) of the line using the formula:
m = (change in y) / (change in x)
Using the values from the table:
m = (10 - (-2)) / (3 - 0) = 12 / 3 = 4
Now that we have the slope, we can find the y-intercept (b) by substituting the values of a point (x, y) from the table into the equation y = mx + b. Let's use the point (0, -2):
-2 = 4 * 0 + b
-2 = b
Therefore, the equation that represents the data in the table is:
y = 4x - 2
This equation represents a linear relationship between x and y, where the slope (m) is 4, and the y-intercept (b) is -2.
assuming linear ... y = m x + b
when x = 0 , y = -2 ... this is the value of b
taking b out of the equation (and the table)
x -6 -1 0 3 5
y -24 -4 0 12 20
y/x is the slope (m)