Which Function Rule Represents the data in the table.
X | Y
-3| -17
-2| -14
-1| -11
0 | -8
1 | -5
A. Y = -3x-8
B. Y = 1/3x -8
C. Y = 3x -8
D. Y = 1/3x+8
AAAaannndd the bot gets it wrong yet again!
C. y = 3x-8
To determine the function rule that represents the given data in the table, we need to look for a pattern by examining the relationship between the x and y values.
Let's start by calculating the difference between the x values:
-2 - (-3) = 1
-1 - (-2) = 1
0 - (-1) = 1
1 - 0 = 1
We can see that the difference between the x values is consistent, indicating that the function of the data is linear.
Next, let's examine the difference between the y values:
-14 - (-17) = 3
-11 - (-14) = 3
-8 - (-11) = 3
-5 - (-8) = 3
We can observe that the difference between the y values is also consistent, confirming that the function is linear.
Lastly, let's find the slope. The slope of a linear function is determined by the change in y divided by the change in x. Let's take any two points from the table:
(-2, -14) and (-3, -17)
Change in y = -14 - (-17) = 3
Change in x = -2 - (-3) = 1
Slope = Change in y / Change in x = 3 / 1 = 3
Now that we have determined that the slope is 3, we can use this information to find the y-intercept. Let's substitute the slope (m) and one of the points into the slope-intercept form equation (y = mx + b) and solve for b:
-14 = 3(-2) + b
-14 = -6 + b
b = -14 + 6
b = -8
Therefore, the function rule that represents the given data in the table is:
Y = 3x - 8
So the correct answer is C. Y = 3x - 8.
To determine which function rule represents the data in the table, we need to analyze the relationship between the values of x and y.
Looking at the table, we can observe that as x increases by 1, y increases by 3. This indicates a constant rate of change. Therefore, the relationship between x and y is linear.
To find the slope, we calculate the change in y divided by the change in x for any two points in the table. Let's choose the points (-3, -17) and (0, -8).
Change in y = -8 - (-17) = 9
Change in x = 0 - (-3) = 3
Slope = change in y / change in x = 9 / 3 = 3
Now that we have the slope, we can substitute it into the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (0, -8), we can substitute x = 0 and y = -8 into the equation:
-8 = 3(0) + b
-8 = 0 + b
b = -8
Therefore, the equation that represents the data in the table is:
Y = 3x - 8
Comparing this equation with the given options, we can conclude that the correct function rule is:
C. Y = 3x - 8