Question

find the rule of the function shown on the table

X= -1, 0, 1, 2
Y= -2, 1, 4, 7

Answer 1

find the solution to the system of equations by using graphing or substitution.
y = 6 - x and y = x - 2

Answer 2

The rule for this function is:

Y = 3X + 1

To confirm this rule, substitute each X value into the equation and verify that it gives the corresponding Y value. For example:

When X = -1, Y = 3(-1) + 1 = -2, which matches the given Y value of -2.
When X = 0, Y = 3(0) + 1 = 1, which matches the given Y value of 1.
When X = 1, Y = 3(1) + 1 = 4, which matches the given Y value of 4.
When X = 2, Y = 3(2) + 1 = 7, which matches the given Y value of 7.

Therefore, the rule Y = 3X + 1 is correct.

Answer 3

To solve the system of equations by substitution, substitute y = x - 2 from the second equation into the first equation:

y = 6 - x
x - 2 = 6 - x
2x = 8
x = 4

Now substitute x = 4 back into either equation to find the value of y:

y = x - 2
y = 4 - 2
y = 2

Therefore, the solution to the system of equations is the ordered pair (4, 2).

To solve the system of equations by graphing, plot the two lines y = 6 - x and y = x - 2 on the same coordinate plane:

```
| +5
| +4 o
| /
| +3 o
| /
| +2 o
| \
| +1 o
| \
| 0 1 2 3 4
---+-----------------
| |
1| | /
| | /
2| | o
| | /
3| o/
| |\
4| | o (4, 2)
| |
|
```

The two lines intersect at the point (4, 2), which is the solution to the system of equations.