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Find the function rule.
x –2 –1 0 1 2
y 9 4 –1 –6 –11
..
To find the function rule, we can examine how the output (y) values change as the input (x) values change. From –2 to –1, the output decreases by 5. From –1 to 0, the output decreases by 5 again. This pattern continues throughout the table, with the output decreasing by 5 each time the input is increased by 1. Therefore, we can write the function rule as:
y = –5x + k
To find the value of k, we can choose any point from the table and substitute its coordinates into the equation. For example, using the point (0, –1):
–1 = –5(0) + k
–1 = k
So the function rule for this table is:
y = –5x – 1
To find the function rule, we will first look for a pattern in the given x and y values.
From the table, we can observe that as the x-values increase by 1, the y-values decrease by 5. This indicates that there is a linear relationship between x and y with a constant rate of change of -5.
To find the function rule, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Using the given x and y values, we can pick any pair of points to calculate the slope.
Let's choose the points (-2, 9) and (-1, 4).
Slope (m) = (y2 - y1) / (x2 - x1)
= (4 - 9) / (-1 - (-2))
= (-5) / (1)
= -5
Now that we have the slope, we can substitute it along with one of the points into the slope-intercept form to find the value of b.
Using the point (-2, 9):
9 = -5(-2) + b
9 = 10 + b
b = 9 - 10
b = -1
Now we can write the function rule:
y = -5x - 1