Find the function rule.
x | -2 | -1 | 0 | 1 | 2
y | 9 | 4 | -1 | -6 | -11
I need to show my work, but I'm not sure what the function rule is. Can someone explain it to me?
y decreases by 5 as x increases by 1 ... the slope of the line is -5
y = -5 x + b ... plug in one of the points to find b
I don't think I put the numbers in very well, but the numbers are:
-2 = 9
-1 = 4
0 = -1
1 = -6
2 = -11
whats b?
To find the function rule, you need to identify the pattern or relationship between the values of x and y. In this case, you can observe that for every increase of 1 in x, the corresponding value of y decreases by 5.
Let's break it down step by step:
Step 1: Look at the values of x and y given in the table.
x | -2 | -1 | 0 | 1 | 2
y | 9 | 4 | -1 | -6 | -11
Step 2: Compare the values of y for consecutive values of x.
The difference between y for -2 and -1 is 9-4 = 5.
The difference between y for -1 and 0 is 4-(-1) = 5.
The difference between y for 0 and 1 is -1-(-6) = 5.
The difference between y for 1 and 2 is -6-(-11) = 5.
Step 3: Identify the pattern or relationship between x and y.
From the observations in Step 2, we can see that for every increase of 1 in x, the corresponding value of y decreases by 5.
Step 4: Write the function rule.
Based on the pattern we identified, we can express the relationship between x and y as y = -5x + c, where c is a constant that we need to find.
To find the constant c, we can substitute one of the given x and y values into the function rule and solve for c.
Let's use the point (0, -1):
-1 = -5(0) + c
-1 = c
So, the function rule is y = -5x - 1.
Remember to double-check by substituting other x and y values from the table into the function rule to make sure they satisfy the equation.