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 Vocabulary Any point on a line is a solution to the linear equation. X/Y Tables You can do a couple of things when this happens. Sometimes an equation will not be in slope-intercept form... 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. And then one more example! yay... 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 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. The x-values are the input values and the y-values are the output values Example 1: Given the equation y=5x-2, which set of numbers complete the table? X Y 0 1 2 3 4 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.) Example 2: X Y 0 1 2 3 4 8 Given the equation x=2y-4 which set of numbers complete the table? 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 4 Step 3: Substitute x for 0, 1, 3, 4 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. Example 3: Given a table, what is the linear equation? x y 1 2 4 6 8 10 -1 1 5 9 13 17 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 0 -3 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. 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.

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# Matching Linear Equations to x/y Tables

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