Construct linear functions from tables | LearnZillion
Solve application problems involving graphs of linear equations. There are multiple ways to represent a linear relationship—a table, a linear graph, and there. Creating tables, graphs and equations to model linear data We call those linear relationships because the graph of the relation creates a line. In this article, we'll represent the same relationship with a table, graph, and equation to see how this works. .. Practice: Linear equations word problems: graphs.
Use numbers like -1, 0, 1, 1. Place the curser in the Y column and push. Discuss what operation s might have been performed on X to get Y. Have students predict what they think the rule might be, and write that as an equation. Tell students you will try their prediction on another value for X.
If their prediction IS the correct equation, the value for Y will be the result. Type another value in the X column and push in the corresponding position in the Y column. Ask students if the same operation s they discussed was used on this new value for X to get the resulting value in the Y column. If not, tell them you want them to find an operation s that could be used for both the first and second X values you showed them to get the resulting Y values.
Have them develop a "rule". Write their rule as an equation. To check their rule, type a third value in the X column. Ask them to perform their rule on that value.
Then press for the corresponding value in the Y column and see if they got the same result. Enter two or three more values in the X column.
Linear Equation Table Of Values. Examples, how to, and Graph
Have students copy the table, write the equation and graph the ordered pairs on the Linear Relations Using Tables, Equations and Graphs worksheet. You may choose not to press for the remaining Y values asking students to substitute the given value for X and find the value for the Y column.
You will need to discuss the minimum and maximum values to be shown for the x and y-axes, so their calculator graphs will look like the graphs on their worksheets. Let's look at a few examples, and it will all make more sense! After substituting those values into the equation: Therefore, the ordered pairs that I found on my graph were: I plotted those points on my graph.
I then used my ruler and drew a straight line through those points. If you had done this problem on your own, you may have found three different points using the table of values.
That's ok, because even if your three points are different, your line will still look exactly the same! We can also find other solutions for the equation just by reading the graph.
I see that 3,7 is a point on the graph. If I substitute 3 for x into the equation, I will get 7 as my y coordinate.
This line goes on forever, so there are infinite solutions to the equation. Let's look at another example. This becomes a little trickier in choosing x coordinates because we could end up with a fraction for the y coordinate. This then becomes a little more difficult to graph.
Using a Table of Values to Graph Linear Equations
So, the trick is to look at the denominator of the coefficient. You want to choose x coordinates that are either multiples of the denominator or 0.
Then choose either the same value as the denominator or a multiple of the denominator. Remember, you also have a choice of positive or negative numbers! This will ensure that your y coordinate is an integer which is much easier to graph. If the coefficient is a fraction, choose 0 or a multiple of the denominator as your x coordinates! Ok, one more example: There are an infinite number of solutions for this graph, as the line goes on forever in both directions. Any point on this line is a solution to the equation.
A Few Notes About Example 3 This example has a slightly different direction, but involves the same process.