x -2 -1 0 1 2 y 9 4 -1 -6 -11 find function rule
looks for every increase of 1 unit in the x's the corresponding y decreases by 5
so slope = -5
y = -5x + b
at x = -2, y = 9
9 = -5(-2) + b
b = -1
function rule:
y = -5x - 1
To find the function rule that relates the values of x and y in this table, we can start by looking for a pattern or relationship between the corresponding x and y values.
By observing the table, we can see that as x increases by 1, y decreases by 5. This suggests that there is a linear relationship between x and y.
To confirm this, we can calculate the slope (rate of change) between any two points in the table. Let's take the first two points (-2, 9) and (-1, 4):
Slope = (y2 - y1) / (x2 - x1)
= (4 - 9) / (-1 - (-2))
= -5 / 1
= -5
The slope between any two points in this table is constant and equal to -5.
Now that we know the slope, we can determine the y-intercept. Let's pick any point from the table, such as (0, -1):
Using the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope, and (x1, y1) is a point on the line.
y - (-1) = -5(x - 0)
y + 1 = -5x
Subtracting 1 from both sides, we get:
y = -5x - 1
Therefore, the function rule that represents the relationship between x and y in this table is y = -5x - 1.
To find the function rule that relates the values of x to the corresponding values of y, we can analyze the given data. Let's take a closer look at the relationship between x and y:
When x = -2, y = 9
When x = -1, y = 4
When x = 0, y = -1
When x = 1, y = -6
When x = 2, y = -11
To determine the pattern or rule, we need to examine how the values of y change as x changes.
Notice that when x increases by 1, y decreases by 5. Therefore, it seems that the function rule might involve multiplying x by -5 and then adding an unknown constant.
Let's test this rule by plugging in the x-values and applying the proposed function rule:
For x = -2: -2 * -5 + C = 9 => 10 + C = 9 => C = -1
For x = -1: -1 * -5 + C = 4 => 5 + C = 4 => C = -1
For x = 0: 0 * -5 + C = -1 => 0 + C = -1 => C = -1
For x = 1: 1 * -5 + C = -6 => -5 + C = -6 => C = -1
For x = 2: 2 * -5 + C = -11 => -10 + C = -11 => C = -1
Since the value of C remains consistent (-1) throughout, we can conclude that the function rule is y = -5x - 1.
Therefore, the function rule that relates x to y is y = -5x - 1.