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

Math
xy-1503112-13-3
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.
5=a(-1)+b3=a(0)+b1=a(1)+b-1=a(2)+b-3=a(3)+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
5=a(-1)+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
Add 0 and b.
3=b
5=a(-1)+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
3=b
5=a(-1)+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
Simplify each term.
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Move -1 to the left of a.
3=b
5=-1⋅a+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
Rewrite -1a as -a.
3=b
5=-a+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
3=b
5=-a+b
1=a(1)+b
-1=a(2)+b
-3=a(3)+b
Multiply a by 1.
3=b
5=-a+b
1=a+b
-1=a(2)+b
-3=a(3)+b
Move 2 to the left of a.
3=b
5=-a+b
1=a+b
-1=2a+b
-3=a(3)+b
Move 3 to the left of a.
3=b
5=-a+b
1=a+b
-1=2a+b
-3=3a+b
3=b
5=-a+b
1=a+b
-1=2a+b
-3=3a+b
Rewrite the equation as b=3.
b=3
5=-a+b
1=a+b
-1=2a+b
-3=3a+b
Replace all occurrences of b with 3 in each equation.
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Replace all occurrences of b in 5=-a+b with 3.
b=3
5=-a+3
1=a+b
-1=2a+b
-3=3a+b
Replace all occurrences of b in 1=a+b with 3.
b=3
5=-a+3
1=a+3
-1=2a+b
-3=3a+b
Replace all occurrences of b in -1=2a+b with 3.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+b
Replace all occurrences of b in -3=3a+b with 3.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
Simplify.
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Remove parentheses.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
Remove parentheses.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
Remove parentheses.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
Remove parentheses.
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
b=3
5=-a+3
1=a+3
-1=2a+3
-3=3a+3
Solve for a in the second equation.
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Rewrite the equation as -a+3=5.
b=3
-a+3=5
1=a+3
-1=2a+3
-3=3a+3
Move all terms not containing a to the right side of the equation.
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Subtract 3 from both sides of the equation.
b=3
-a=5-3
1=a+3
-1=2a+3
-3=3a+3
Subtract 3 from 5.
b=3
-a=2
1=a+3
-1=2a+3
-3=3a+3
b=3
-a=2
1=a+3
-1=2a+3
-3=3a+3
Multiply each term in -a=2 by -1
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Multiply each term in -a=2 by -1.
b=3
(-a)⋅-1=2⋅-1
1=a+3
-1=2a+3
-3=3a+3
Multiply (-a)⋅-1.
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Multiply -1 by -1.
b=3
1a=2⋅-1
1=a+3
-1=2a+3
-3=3a+3
Multiply a by 1.
b=3
a=2⋅-1
1=a+3
-1=2a+3
-3=3a+3
b=3
a=2⋅-1
1=a+3
-1=2a+3
-3=3a+3
Multiply 2 by -1.
b=3
a=-2
1=a+3
-1=2a+3
-3=3a+3
b=3
a=-2
1=a+3
-1=2a+3
-3=3a+3
b=3
a=-2
1=a+3
-1=2a+3
-3=3a+3
Replace all occurrences of a with -2 in each equation.
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Replace all occurrences of a in 1=a+3 with -2.
b=3
a=-2
1=(-2)+3
-1=2a+3
-3=3a+3
Replace all occurrences of a in -1=2a+3 with -2.
b=3
a=-2
1=(-2)+3
-1=2(-2)+3
-3=3a+3
Replace all occurrences of a in -3=3a+3 with -2.
b=3
a=-2
1=(-2)+3
-1=2(-2)+3
-3=3(-2)+3
b=3
a=-2
1=(-2)+3
-1=2(-2)+3
-3=3(-2)+3
Simplify.
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Add -2 and 3.
b=3
a=-2
1=1
-1=2(-2)+3
-3=3(-2)+3
Simplify 2(-2)+3.
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Multiply 2 by -2.
b=3
a=-2
1=1
-1=-4+3
-3=3(-2)+3
Add -4 and 3.
b=3
a=-2
1=1
-1=-1
-3=3(-2)+3
b=3
a=-2
1=1
-1=-1
-3=3(-2)+3
Simplify 3(-2)+3.
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Multiply 3 by -2.
b=3
a=-2
1=1
-1=-1
-3=-6+3
Add -6 and 3.
b=3
a=-2
1=1
-1=-1
-3=-3
b=3
a=-2
1=1
-1=-1
-3=-3
b=3
a=-2
1=1
-1=-1
-3=-3
Since 1=1, the equation will always be true.
b=3
a=-2
Always true
-1=-1
-3=-3
Remove any equations from the system that are always true.
b=3
a=-2
-1=-1
-3=-3
Since -1=-1, the equation will always be true.
b=3
a=-2
Always true
Always true
-3=-3
Remove any equations from the system that are always true.
b=3
a=-2
-3=-3
Since -3=-3, 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=-1.
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Multiply -2 by -1.
y=2+3
Add 2 and 3.
y=5
y=5
If the table has a linear function rule, y=y for the corresponding x value, x=-1. This check passes since y=5 and y=5.
5=5
Calculate the value of y when a=-2, b=3, and x=0.
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Multiply -2 by 0.
y=0+3
Add 0 and 3.
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
Add -2 and 3.
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
Add -4 and 3.
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
Add -6 and 3.
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
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],[-1,5],[0,3],[1,1],[2,-1],[3,-3]]

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