Module 2  Lines  
Introduction  Lesson 1  Lesson 2  Lesson 3  Self Test  
Lesson 2.1: Equations of Lines  
There are several ways to write an equation of a line. In this lesson you will use the pointslope form of a line to create a graph. You will investigate the relationship between perpendicular lines and adjust the calculator's Viewing Window so that the lines look perpendicular. Slope The slope of the line through the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by For example the slope of the line through the points (1, 2) and (2, 3) is PointSlope Form of a Line The pointslope form of the line with slope m that passes through a point (x_{1}, y_{1}) is The line that passes through the points (1, 2) and (2, 3) has slope and its equation can be written using either point for (x1,y1). or Both equations represent the same line. Graphing a Line
Viewing Window References The following notation will be used to represent the window settings: The first triplet of values represents Xmin, Xmax and Xscl and the second triplet of values represents the corresponding Yparameters. The TRACE Cursor The TRACE cursor may be used to move the cursor from one plotted point to the next along a function's graph. The cursor's coordinates are displayed at the bottom of the screen and the cursor can be moved along the graph by using the left and right arrow keys. The function is displayed in the topleft corner of the screen.
The cursor appears on the line, the cursor coordinates appear at the bottom of the screen, and the corresponding function appears at the top of the screen. Notice the cursor cannot be placed directly on the point with xcoordinate x = 1 by using the left and right arrow keys. Entering TRACE Values Directly You may place the TRACE cursor at a specific point by directly entering the point's xvalue.
The yvalue is 2 when the xvalue is 1, as shown at the bottom of the screen. The point (1, 2) is on the line. 2.1.1 Place the TRACE cursor directly on the point where x = 2 and determine the corresponding yvalue. Click here for the answer. The TRACE cursor shows that the line passes through the point (2, 3). Slopes of Perpendicular Lines If two nonvertical lines are perpendicular, then their slopes are negative reciprocals of each other. That is, if m is the slope of a line, then any line perpendicular to it will have slope Finding Equations of Perpendicular Lines Suppose you want an equation of the line passing through (1, 2) that is perpendicular to the line The slope of the desired perpendicular line is because the slope of the original line is Using the pointslope form with and point (1, 2), the point slope equation of the perpendicular line is Graphing Perpendicular Lines
Using A Square Window Notice the lines do not appear to be perpendicular in the window above because the units along the xaxis are larger than the units along the yaxis. The Viewing Window may be redefined by selecting ZSquare from the Zoom menu. Selecting a Zoom Square window makes units of equal length on both axes and will make the lines appear perpendicular.
The Zoom menu's ZSquare feature adjusts the viewing window so that the lines appear perpendicular. 2.1.2 What are the Viewing Window values of the above Viewing Window? Click here for the answer.


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