Find the Function Rule table[[x,y],[0,-3],[1,-1],[2,1],[3,3],[4,5]]

Math
xy0-31-1213345
Check if the function rule is linear.
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To find if the table follows a function rule, check to see if the values follow the linear form y=ax+b.
y=ax+b
Build a set of equations from the table such that y=ax+b.
-3=a(0)+b-1=a(1)+b1=a(2)+b3=a(3)+b5=a(4)+b
Calculate the values of a and b.
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Simplify each equation.
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Simplify a(0)+b.
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Multiply a by 0.
-3=0+b
-1=a(1)+b
1=a(2)+b
3=a(3)+b
5=a(4)+b
Add 0 and b.
-3=b
-1=a(1)+b
1=a(2)+b
3=a(3)+b
5=a(4)+b
-3=b
-1=a(1)+b
1=a(2)+b
3=a(3)+b
5=a(4)+b
Multiply a by 1.
-3=b
-1=a+b
1=a(2)+b
3=a(3)+b
5=a(4)+b
Move 2 to the left of a.
-3=b
-1=a+b
1=2a+b
3=a(3)+b
5=a(4)+b
Move 3 to the left of a.
-3=b
-1=a+b
1=2a+b
3=3a+b
5=a(4)+b
Move 4 to the left of a.
-3=b
-1=a+b
1=2a+b
3=3a+b
5=4a+b
-3=b
-1=a+b
1=2a+b
3=3a+b
5=4a+b
Rewrite the equation as b=-3.
b=-3
-1=a+b
1=2a+b
3=3a+b
5=4a+b
Replace all occurrences of b with -3 in each equation.
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Replace all occurrences of b in -1=a+b with -3.
b=-3
-1=a-3
1=2a+b
3=3a+b
5=4a+b
Replace all occurrences of b in 1=2a+b with -3.
b=-3
-1=a-3
1=2a-3
3=3a+b
5=4a+b
Replace all occurrences of b in 3=3a+b with -3.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a+b
Replace all occurrences of b in 5=4a+b with -3.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
Simplify.
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Remove parentheses.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
Remove parentheses.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
Remove parentheses.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
Remove parentheses.
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
b=-3
-1=a-3
1=2a-3
3=3a-3
5=4a-3
Solve for a in the second equation.
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Rewrite the equation as a-3=-1.
b=-3
a-3=-1
1=2a-3
3=3a-3
5=4a-3
Move all terms not containing a to the right side of the equation.
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Add 3 to both sides of the equation.
b=-3
a=-1+3
1=2a-3
3=3a-3
5=4a-3
Add -1 and 3.
b=-3
a=2
1=2a-3
3=3a-3
5=4a-3
b=-3
a=2
1=2a-3
3=3a-3
5=4a-3
b=-3
a=2
1=2a-3
3=3a-3
5=4a-3
Replace all occurrences of a with 2 in each equation.
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Replace all occurrences of a in 1=2a-3 with 2.
b=-3
a=2
1=2(2)-3
3=3a-3
5=4a-3
Replace all occurrences of a in 3=3a-3 with 2.
b=-3
a=2
1=2(2)-3
3=3(2)-3
5=4a-3
Replace all occurrences of a in 5=4a-3 with 2.
b=-3
a=2
1=2(2)-3
3=3(2)-3
5=4(2)-3
b=-3
a=2
1=2(2)-3
3=3(2)-3
5=4(2)-3
Simplify.
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Simplify 2(2)-3.
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Multiply 2 by 2.
b=-3
a=2
1=4-3
3=3(2)-3
5=4(2)-3
Subtract 3 from 4.
b=-3
a=2
1=1
3=3(2)-3
5=4(2)-3
b=-3
a=2
1=1
3=3(2)-3
5=4(2)-3
Simplify 3(2)-3.
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Multiply 3 by 2.
b=-3
a=2
1=1
3=6-3
5=4(2)-3
Subtract 3 from 6.
b=-3
a=2
1=1
3=3
5=4(2)-3
b=-3
a=2
1=1
3=3
5=4(2)-3
Simplify 4(2)-3.
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Multiply 4 by 2.
b=-3
a=2
1=1
3=3
5=8-3
Subtract 3 from 8.
b=-3
a=2
1=1
3=3
5=5
b=-3
a=2
1=1
3=3
5=5
b=-3
a=2
1=1
3=3
5=5
Since 1=1, the equation will always be true.
b=-3
a=2
Always true
3=3
5=5
Remove any equations from the system that are always true.
b=-3
a=2
3=3
5=5
Since 3=3, the equation will always be true.
b=-3
a=2
Always true
Always true
5=5
Remove any equations from the system that are always true.
b=-3
a=2
5=5
Since 5=5, the equation will always be true.
b=-3
a=2
Always true
Always true
Always true
Remove any equations from the system that are always true.
b=-3
a=2
List the solutions to the system of equations.
b=-3
a=2
Always true
Always true
Always true
List all of the solutions.
b=-3a=2
b=-3a=2
Calculate the value of y using each x value in the relation and compare this value to the given y value in the relation.
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Calculate the value of y when a=2, b=-3, and x=0.
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Multiply 2 by 0.
y=0-3
Subtract 3 from 0.
y=-3
y=-3
If the table has a linear function rule, y=y for the corresponding x value, x=0. This check passes since y=-3 and y=-3.
-3=-3
Calculate the value of y when a=2, b=-3, and x=1.
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Multiply 2 by 1.
y=2-3
Subtract 3 from 2.
y=-1
y=-1
If the table has a linear function rule, y=y for the corresponding x value, x=1. This check passes since y=-1 and y=-1.
-1=-1
Calculate the value of y when a=2, b=-3, and x=2.
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Multiply 2 by 2.
y=4-3
Subtract 3 from 4.
y=1
y=1
If the table has a linear function rule, y=y for the corresponding x value, x=2. This check passes since y=1 and y=1.
1=1
Calculate the value of y when a=2, b=-3, and x=3.
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Multiply 2 by 3.
y=6-3
Subtract 3 from 6.
y=3
y=3
If the table has a linear function rule, y=y for the corresponding x value, x=3. This check passes since y=3 and y=3.
3=3
Calculate the value of y when a=2, b=-3, and x=4.
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Multiply 2 by 4.
y=8-3
Subtract 3 from 8.
y=5
y=5
If the table has a linear function rule, y=y for the corresponding x value, x=4. This check passes since y=5 and y=5.
5=5
Since y=y for the corresponding x values, the function is linear.
The function is linear
The function is linear
The function is linear
Since all y=y, the function is linear and follows the form y=2x-3.
y=2x-3
Find the Function Rule table[[x,y],[0,-3],[1,-1],[2,1],[3,3],[4,5]]

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