What is the equation of the function rule that models the data represented in the table below?
X: 3 | 6 | 9 | 12 |
Y: 5 | 10 | 15 | 20 |
To find the equation of the function rule that models the data in the table, we need to observe the pattern and relationship between the input values (x) and the output values (y).
Looking at the table, we can see that for every x value, the corresponding y value is obtained by multiplying the x value by 5.
So, we can write the equation as:
y = 5x
Therefore, the equation of the function rule that models the data in the table is y = 5x.
To find the equation of the function rule that models the data in the table, we need to examine the relationship between the values of X and Y.
Notice that as X increases by 3 each time, Y also increases by 5. This suggests that the relationship between X and Y is linear.
To find the equation, we can use the slope-intercept form of a linear equation, which is:
Y = mx + b
where m represents the slope of the line, and b represents the y-intercept.
To determine the slope, we can calculate the change in Y divided by the change in X for any two points on the line. Let's use the first two points (3, 5) and (6, 10):
Slope (m) = (10 - 5) / (6 - 3)
= 5 / 3
Now that we have the slope (m), we can substitute it into the equation:
Y = (5/3)x + b
Next, we need to find the y-intercept (b). We can do this by choosing any point on the line and substituting its coordinates into the equation. Let's use the point (3, 5):
5 = (5/3)(3) + b
Now let's solve for b:
5 = 5 + b
b = 5 - 5
b = 0
Therefore, the equation of the function rule that models the data is:
Y = (5/3)x + 0
Y = (5/3)x