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.
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.
To complete the table using the function rule -10x + y = 4, we substitute the given values of x into the equation and solve for the corresponding values of y.
Starting with the first value of x, which is -2:
-10(-2) + y = 4
20 + y = 4
y = 4 - 20
y = -16
For the second value of x, which is -1:
-10(-1) + y = 4
10 + y = 4
y = 4 - 10
y = -6
Continuing with the third value of x, which is 0:
-10(0) + y = 4
0 + y = 4
y = 4
For the fourth value of x, which is 1:
-10(1) + y = 4
-10 + y = 4
y = 4 + 10
y = 14
Finally, for the fifth value of x, which is 2:
-10(2) + y = 4
-20 + y = 4
y = 4 + 20
y = 24
So, the completed table is:
x -2 -1 0 1 2
y -16 -6 4 14 24