Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

x
−
2
−
1
0 1 2
y
Use the function rule to complete the table.

−
10
x
+
y
=
4
explain in words and details please.

Answer 1

To complete the table using the function rule, we need to figure out what the rule or equation is that relates the values of x and y. We can do this by looking at the pattern or trend in the given values.

From the table, we can see that when x is -2, y is -10. When x is -1, y is -6. And when x is 0, y is -2. We can also observe that as x increases by 1, y increases by 4.

This information suggests that the function rule is a linear equation in the form y = mx + b, where m is the slope or rate of change and b is the y-intercept. To find the values of m and b, we can use any of the given points (x, y) and plug them into the equation.

Let's use the point (-1, -6):

-10 + y = 4(-2)
y + 10 = -8
y = -18

Therefore, the equation for the function rule is y = 4x - 2. We can use this equation to complete the rest of the table:

x y
-2 -10
-1 -6
0 -2
1 2
2 6

To explain in words and detail, we used the given table to identify the pattern or relationship between the values of x and y. We recognized that this pattern can be described by a linear equation, y = mx + b, and found the values of m and b by solving for them using one of the given points. With the equation, we were able to fill in the missing values of y in the table.