Explain how to write a function rule from the table below. Then write a function rule.
x 2 4 6
y 1 0 -1
To write a function rule from a table, you need to identify the relationship between the input (x-values) and the output (y-values). In this case, when the x-value doubles, the y-value decreases by 1.
To write the function rule, we can start by finding the pattern. From the table, we can see that the x-values increase by 2 each time, and the y-values decrease by 1 each time. This indicates that the function is linear.
To represent this relationship mathematically, we can use the equation:
y = mx + b
where y is the output (y-value), x is the input (x-value), m is the slope (change in y over change in x), and b is the y-intercept (the point where the graph intersects the y-axis).
Using the given table, we can calculate the slope (m) by dividing the change in y (1 to 0) by the change in x (2 to 4). This gives us:
m = (0 - 1) / (4 - 2) = -1/2
Now we can substitute the slope (m) into the equation:
y = (-1/2)x + b
To find the y-intercept (b), we can choose any point from the table and substitute the values of x and y into the equation. Let's use the first point (2, 1):
1 = (-1/2)(2) + b
Now we can solve for b:
1 = -1 + b
b = 2
Therefore, the function rule for the given table is:
y = (-1/2)x + 2