Introduction[ edit ] The shortest path between two given points in a curved space, assumed to be a differential manifoldcan be defined by using the equation for the length of a curve a function f from an open interval of R to the spaceand then minimizing this length between the points using the calculus of variations. This has some minor technical problems, because there is an infinite dimensional space of different ways to parameterize the shortest path.

Show students that in order to graph those linear relationships, you had to type an algebraic rule or an equation into the graphing calculator for each.

Have the students write the equations on bottom of the journal page. Do this for B, C, and D. Point out that all four equations have a y and x dependent and independent variable, and that there are no exponents in the expression.

Ask students in each small group to look at the equation for graph A and think about how the equation describes how y relates to x. After discussion an equation rulehave the students choose a number for X and together use the equation to find Y without looking at the table on the calculator.

Choose two or three numbers for x they did not use in their tables on the journal page. Cooperative Sharing Game-Red Rover: Practice using the equation to find values for Y by playing Red Rover where teams choose a person to come to their team to explain the rule and show how the new ordered pair was created by using that rule.

In Red Rover, students work with their own team for a minute. Then, each team calls a person from another team to come over to their table to sit down and explain what was done. If not, the team they visit earns the 2 points. How can a graph, a table, an equation or ordered pairs help you describe the relationship between two variables?

How is graphing a linear equation from ordered pairs similar to graphing a linear equation using a table? Use the following TI activity to work with the students to write an equation for the relationship for x and y using a table to identify the pattern, and then graph that relation.

Select and set the dependent and independent variables to Aask. Select and type a value in the X column.

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.

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.

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. Some possible linear equations you may wish to try might be:Ask Math Questions you want answered Share your favorite Solution to a math problem Share a Story about your experiences with Math which could inspire or help others.

By graphing the lines of a system of two linear equations with two variables, you can determine the possible number of solutions. Scroll through the Observations using ~ (| to review, if necessary).

Read each screen carefully. When you come to a Write an Observation screen, stop and write the answer to the question on your worksheet.

Observation 1. Equation: x = a 2. The graph is a line parallel to the y-axis and passes through the x-intercept (a, 0). 3. All the x-coordinates on the line are a. 4. The slope of a vertical line is undefined. Example 7: Graph x 2 Graphing and Writing Linear Equations Author.

Transform the given function f(x) as described and write the resulting function as an equation. 5) f (x) x expand vertically by a factor of.

Jan 11, · Shows how to write the equation of a line in the slope intercept from from the graph of the line. You can link to all my videos at my website: caninariojana.com ©n mK7uEtkaS JSro ZfvtawaaCr5ei rLoLVCA.m K kAzlxlq Qr1iMg8hntqs5 arReNsJe8rFvieRd8.Z G ZMbaZdDeZ uw7ityhw gI7nfxiYnPi9tXeP HArlygkeubwraal caninariojana.comheet by Kuta Software LLC Answers to Graphing Linear Equations Using a Table of Values (ID: 1).

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