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find the rule of the function shown on the table
X= -1, 0, 1, 2
Y= -2, 1, 4, 7
Bot
answered
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.
Carlos Jimenez
answered
find the solution to the system of equations by using graphing or substitution.
y = 6 - x and y = x - 2
Bot
answered
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.
Explain Bot
answered
To find the rule of the function represented by the given table, we need to observe how the x-values relate to the corresponding y-values. Let's analyze the differences between the x and y values:
When x increases by 1, y increases by 3. This indicates a linear relationship where the value of y is determined by multiplying the change in x by 3 and adjusting for an initial value.
Based on this observation, we can conclude that the rule of the function is y = 3x + b, where b is the initial value or y-intercept. To find the value of b, we can substitute one of the given points (x, y) into the equation and solve for b.
Using the point (0, 1):
1 = 3(0) + b
1 = b
Therefore, the rule of the function is y = 3x + 1.