Write the linear equation that gives the rule for this table.
2 -55
3 -37
4 -19
5 -1
The linear equation that gives the rule for this table is y = 18x - 91.
To write a linear equation using the given table, we need to find the pattern in the data. We can do this by calculating the difference between the values of the y-coordinates (the second column).
Looking at the differences:
-37 - (-55) = 18
-19 - (-37) = 18
-1 - (-19) = 18
We can see that the difference between the y-coordinates is constant at 18. So, we know that the slope of the equation will be 18.
Now, we need to find the y-intercept. We can do this by substituting one of the points into the equation and solving for the y-intercept.
Using the point (2, -55):
-55 = 18(2) + b
-55 = 36 + b
b = -91
Therefore, the linear equation that gives the rule for this table is:
y = 18x - 91
To write the linear equation, we need to identify the pattern or relationship between the given values in the table. In a linear equation, we usually have the form y = mx + b, where y represents the output (in this case, the second column values), x represents the input (in this case, the first column values), m represents the slope, and b represents the y-intercept.
Let's look at the difference between consecutive y-values:
-55 - (-37) = -55 + 37 = -18
-37 - (-19) = -37 + 19 = -18
-19 - (-1) = -19 + 1 = -18
We observe that the difference between consecutive y-values is constant (-18). This tells us that the relationship between the x-values and y-values is a constant rate of change. The y-values are decreasing by 18 as the x-values increase by 1.
Now, let's find the y-intercept. We can pick any point from the table. Let's choose (2, -55):
y = mx + b
-55 = 2m + b
To find the slope (m), we can calculate the change in y divided by the change in x using any two points. Let's use (2, -55) and (3, -37):
m = (y2 - y1) / (x2 - x1)
= (-37 - (-55)) / (3 - 2)
= (-37 + 55) / (3 - 2)
= 18 / 1
= 18
Now that we have the slope (m = 18) and a point (2, -55), we can substitute these values into the equation to solve for the y-intercept (b).
-55 = 2m + b
-55 = 2(18) + b
-55 = 36 + b
-55 - 36 = b
-91 = b
Therefore, the linear equation that gives the rule for this table is:
y = 18x - 91