Linear equations: Graphical and analytical relationships

30 LECoordn Given a point on a graph, read its X and Y coordinates. Given the coordinates, plot the point on a graph. Includes negative coordinates. Students should be cautioned that the grid points for X=0 and Y=0 are slightly off of the axes.

31 LEDefine The introductory screens present the definitions for slope, which most students will not struggle through. The program displays a linear equation and asks the student to chose 4 values for X. The program calculates the values of Y that are required by the equation and displays the corresponding points in the X-Y plane. The student is then asked to determine the slope and Y-intercept from the graph.

32 LEMxPlsB This program is similar to LEDEFINE, except that it asks the student to read the slope and Y-intercept from the graph and then input the equation in the form Y=mX+b.

33 LESolveY The student must put the displayed equation into slope-intercept form. The screen will display three points which are solutions to the displayed equation and then the line graph of the students equation. If the student's equation is correct , the line will pass through the points.

34 LEWordp1 The screen presents a word description which the student must convert into a linear equation. It may help to suggest to students that they start with the unknown and work backward (or forward as necessary) from there. Then three points must be plotted which satisfy the word description. The line graph of the equation will be displayed and will pass through the points if they are plotted correctly. This program helps make clear to students that "Y=" means "Use this rule to find Y".

35 LETable A linear equation is presented in irregular form. The student is asked to find and enter the slope and Y-intercept. The screen then displays the equation in slope intercept form, using the students values, and asks for values of Y, given that X is -1, 0, and 1. The points are displayed. Then the line graph of the equation will be displayed and will pass through the points if they are plotted correctly. Emphasizes that equal increments to X yield equal increments to Y.

36 LEGraphs Calculate and plot any two solutions to the given linear equation. The solution line will appear, and will pass through the points if they were correct. The intercepts are probably the easiest to find, but perhaps that should be left for the student to discover. The program will allow an error of 0.15 in point placement because of the low resolution of the screen pixels. If an error is recognized after the first point is plotted, it can be erased by placing the cursor on the point and pressing enter.

37 LEIntrcp Calculate and plot the X and Y intercepts for the given linear equation. The solution line will appear, and will pass through the points if they were correct. If an error is recognized after the first point is plotted, it can be erased by placing the cursor on the point and pressing enter.

38 LEPtSlp1 Given a point on a graph and a required slope, the student must find the slope-intercept form of the equation. It is a good opportunity for the student to visualize whether the calculated value of the Y-intercept is consistent with the given point and slope.

39 LE2PtSlp The definition of slope is used to develop an expression for the slope of a line between two points. The student must then find the slope of the line between two points which are specified either by their coordinate pairs, or by points on a graph.

40 LEPtSlp2 Given a point on a graph and a required slope, the student must find the point-slope form of the equation. The derivation from the definition of slope is given on the screen, but the substitution of the general point X,Y for one of the particular points Xsub2,Ysub2 is not explained.

41 LEWordP2 Word problems are presented for which the student most find the appropriate equation. Then a graph of the equation is presented and the student is asked to read the graph to find the value of the dependent value which corresponds to a specified value of the independent value. The student can use the cursor keys to move the cursor to the desired point and then read the trace values at the bottom of the graph. Students should be cautioned to write down the pertinent figures on each screen because they will be needed on a later screen.

42 LERodeo This program is written in a game format. There are five progressively more challenging "rodeo rings", each requiring that the participant "throw a line" to rope two bulls. The rings are identified as "Kiddie", "Greenhorn", "Tenderfoot", "Cowhand", and "Champ". There are four events in each ring. Failure at any event causes the rank to slip back one place. Succeeding at all four events in the "Champ" ring causes a special display, crowning the "Grand Champion".

45 AbsEq2Gr Given a complex absolute value equation, the student is asked to locate the vertex of the needed graph and then put a point on each of its branches. As with most programs requiring more than one point, if an error is made, it can be erased by putting a second point on top of it.

46 AbsGr2Eq Given the graph of an absolute value function, the student is asked to find its equation. The screen will present the graph of the student's equation, followed by the correct graph. Hopefully, one will be superimposed on the other.