Matching Linear Equations to x/y Tables

Matching Linear Equations to x/y Tables

Ordered Pair- two numbers paired together in the form of (x,y) to represent a point on a graph

Linear Equation- An equation between two variables that gives a straight line when plotted on a graph.

Coordinate Plane- specifies each point uniquely in a plane by a pair of numerical coordinates

Input Value (domain) (x)- The number or value that is entered in an x/y table

Output Value (range) (y)-The number or value that is entered in an x/y table

Any point on a line is a solution to the linear equation.

Several solutions can be used to graph a line on a coordinate plane.

You can use an

input-output table

to find the points

of a line by isolating

either the x or

y values.

Step 1: Substitute the domain values into the equation.

y=5x-2

y=5(2)-2

y=10-2

y=8

Step 2: Find all other y values.

{-2, 3, 8, 13, 18}

Step 3: Fill in the table.

You can do a couple of things when this happens.

1.) Form the equation into slope-intercept form by moving x and y

2.) Substitute x for the domain like before and then solve for y. (However, then you would have to isolate y every time.)

Step 1: Choose a method. By choosing the option of forming the equation into slope-intercept form, you would move x and y to the other side of the equation.

Step 2: Isolate Y.

x=2y-4

-y -y

x-y=2-4

-x -x

-y=-2-x

/-1 /-1

y=x+2

Step 3: Substitute x for 0, 1, 3, 4

In multiple choice, you are either asked to find the correct table given an equation, given an equation and you have to choose from a set of numbers given for the output, or finding the equation of a table.

Since the other two examples were filling in a table (and for lack of space and laziness on my part), this example will be matching the equation to the table.

Step 1: Find slope.

Slope formula is (y2-y1)/(x2-x1).

Use two points and substitute their y and x.

(1,-1) (2,1)

(1--1)/(2-1)= (1+1)/(2-1)= 2/1= 2

m=2

Step 2: Find y-intercept.

(o,-3)

b=-3

Step 3: Make the linear equation

y=mx+b

y=2x+-3

y=2x-3

Note: on multiple choice, you will be given a list of equations and can substitute ALL of the x and y values until one does not work or they ALL work.

And then one more example! yay...

Vocabulary

X/Y Tables

The x-values are the input values and the y-values are the output values

Sometimes an equation will not be in slope-intercept form...

4

Given the equation y=5x-2, which set of numbers complete the table?

3

2

1

8

0

X

Example 1:

Y

Example 3:

x

y

Given a table, what is the linear equation?

0

-3

1

-1

2

1

4

5

6

9

8

13

10

17

Example 2:

Given the equation x=2y-4 which set of numbers complete the table?

1

3

4

2

0

X

4

Y