# Find the Function Rule table[[x,y],[-1,8],[0,4],[1,0],[2,-4]] xy-1804102-4
Check if the function rule is linear.
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.
8=a(-1)+b4=a(0)+b0=a(1)+b-4=a(2)+b
Calculate the values of a and b.
Simplify each equation.
Simplify a(0)+b.
Multiply a by 0.
4=0+b
8=a(-1)+b
0=a(1)+b
-4=a(2)+b
4=b
8=a(-1)+b
0=a(1)+b
-4=a(2)+b
4=b
8=a(-1)+b
0=a(1)+b
-4=a(2)+b
Simplify each term.
Move -1 to the left of a.
4=b
8=-1⋅a+b
0=a(1)+b
-4=a(2)+b
Rewrite -1a as -a.
4=b
8=-a+b
0=a(1)+b
-4=a(2)+b
4=b
8=-a+b
0=a(1)+b
-4=a(2)+b
Multiply a by 1.
4=b
8=-a+b
0=a+b
-4=a(2)+b
Move 2 to the left of a.
4=b
8=-a+b
0=a+b
-4=2a+b
4=b
8=-a+b
0=a+b
-4=2a+b
Rewrite the equation as b=4.
b=4
8=-a+b
0=a+b
-4=2a+b
Replace all occurrences of b with 4 in each equation.
Replace all occurrences of b in 8=-a+b with 4.
b=4
8=-a+4
0=a+b
-4=2a+b
Replace all occurrences of b in 0=a+b with 4.
b=4
8=-a+4
0=a+4
-4=2a+b
Replace all occurrences of b in -4=2a+b with 4.
b=4
8=-a+4
0=a+4
-4=2a+4
b=4
8=-a+4
0=a+4
-4=2a+4
Simplify.
Remove parentheses.
b=4
8=-a+4
0=a+4
-4=2a+4
Remove parentheses.
b=4
8=-a+4
0=a+4
-4=2a+4
Remove parentheses.
b=4
8=-a+4
0=a+4
-4=2a+4
b=4
8=-a+4
0=a+4
-4=2a+4
Solve for a in the second equation.
Rewrite the equation as -a+4=8.
b=4
-a+4=8
0=a+4
-4=2a+4
Move all terms not containing a to the right side of the equation.
Subtract 4 from both sides of the equation.
b=4
-a=8-4
0=a+4
-4=2a+4
Subtract 4 from 8.
b=4
-a=4
0=a+4
-4=2a+4
b=4
-a=4
0=a+4
-4=2a+4
Multiply each term in -a=4 by -1
Multiply each term in -a=4 by -1.
b=4
(-a)⋅-1=4⋅-1
0=a+4
-4=2a+4
Multiply (-a)⋅-1.
Multiply -1 by -1.
b=4
1a=4⋅-1
0=a+4
-4=2a+4
Multiply a by 1.
b=4
a=4⋅-1
0=a+4
-4=2a+4
b=4
a=4⋅-1
0=a+4
-4=2a+4
Multiply 4 by -1.
b=4
a=-4
0=a+4
-4=2a+4
b=4
a=-4
0=a+4
-4=2a+4
b=4
a=-4
0=a+4
-4=2a+4
Replace all occurrences of a with -4 in each equation.
Replace all occurrences of a in 0=a+4 with -4.
b=4
a=-4
0=(-4)+4
-4=2a+4
Replace all occurrences of a in -4=2a+4 with -4.
b=4
a=-4
0=(-4)+4
-4=2(-4)+4
b=4
a=-4
0=(-4)+4
-4=2(-4)+4
Simplify.
b=4
a=-4
0=0
-4=2(-4)+4
Simplify 2(-4)+4.
Multiply 2 by -4.
b=4
a=-4
0=0
-4=-8+4
b=4
a=-4
0=0
-4=-4
b=4
a=-4
0=0
-4=-4
b=4
a=-4
0=0
-4=-4
Since 0=0, the equation will always be true.
b=4
a=-4
Always true
-4=-4
Remove any equations from the system that are always true.
b=4
a=-4
-4=-4
Since -4=-4, the equation will always be true.
b=4
a=-4
Always true
Always true
Remove any equations from the system that are always true.
b=4
a=-4
List the solutions to the system of equations.
b=4
a=-4
Always true
Always true
List all of the solutions.
b=4a=-4
b=4a=-4
Calculate the value of y using each x value in the relation and compare this value to the given y value in the relation.
Calculate the value of y when a=-4, b=4, and x=-1.
Multiply -4 by -1.
y=4+4
y=8
y=8
If the table has a linear function rule, y=y for the corresponding x value, x=-1. This check passes since y=8 and y=8.
8=8
Calculate the value of y when a=-4, b=4, and x=0.
Multiply -4 by 0.
y=0+4
y=4
y=4
If the table has a linear function rule, y=y for the corresponding x value, x=0. This check passes since y=4 and y=4.
4=4
Calculate the value of y when a=-4, b=4, and x=1.
Multiply -4 by 1.
y=-4+4
y=0
y=0
If the table has a linear function rule, y=y for the corresponding x value, x=1. This check passes since y=0 and y=0.
0=0
Calculate the value of y when a=-4, b=4, and x=2.
Multiply -4 by 2.
y=-8+4
y=-4
y=-4
If the table has a linear function rule, y=y for the corresponding x value, x=2. This check passes since y=-4 and y=-4.
-4=-4
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=-4x+4.
y=-4x+4
Find the Function Rule table[[x,y],[-1,8],[0,4],[1,0],[2,-4]]     