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Lesson 13

Graphing linear equations

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Graphing equations in 2 variables

• 1) Construct a table of values. Choose a reasonable value for x and solve the equation for y. Repeat this step 3 times.

• 2) Plot the points represented by the solutions to the equation

• 3) Connect the points to form a line. extend the line and draw arrows on the ends to indicate the line extends to infinity.

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Graphing using intercepts

• The points where the graph intersects the axes on the coordinate plane are called

the intercepts.• The point where the graph intersects

the x-axis is called the x- intercept.

• The point where the graph intercepts the y-axis is called the y-intercept.

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Graphing using intercepts

• To find the x-intercept, let y = o, solve the equation for x.

• To find the y-intercept, let x=0, solve the equation for y

• Plot and connect the intercepts.

• Extend the line and add arrows to the ends

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Slope of a line

• The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run).

• m = y2-y1= rise

• x2-x1 run

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Slope intercept form of a linear equation

• A linear equation written in the form

• y=m x +b is written in slope -intercept form, where m is the slope of the line, and b is the y-intercept

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Moving from point to point using the slope

• Positive slope up or down

• right left

• Negative slope up or down

• left right

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practice• 1) Graph the equation y=-1/2 x + 3• A) by constructing a table of values• B) using the intercepts• C) using the slope and y-intercept• 2) graph -x +4y=8• A) by constructing a table of values• B) using the intercepts• C) using the slope and y-intercept• 3) calculate the slope of the lines that contain the following

points:• (-3,5)(5,6) (0,4)(-2,0) (-4,3)(8,3)

•

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Lab 3Calculating points on a graph

• 1. enter the equation into the Y= editor on your calculator

• 2. graph the equation• 3. to calculate the y-values, press 2nd trace to open the

CALC menu, and select 1:value and press ENTER. (the x and y values will be displayed at the bottom)

• 4. calculate the zero by pressing 2nd trace and select 2:zero , then use the arrow keys to move the cursor to the left of the zero and press ENTER. Move the cursor to the right of the zero and press ENTER. Move the cursor to the approximate location of the zero and press ENTER. The zero will be displayed at the bottom of the screen and highlighted on the graph

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Calculate minimum and maximum points and intersection points

• Follow steps on page 85

• PRACTICE:

• Find the zero of y=-17x+51

• Find the maximum of the parabola y=-x2-4x+5

• Find the intersection of y=-x+2 and y=-5x-1

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Lab 4 changing the window and line of a graph

To center the window on the vertex, locate the vertex and see how much the x and y values are moved from the origin.

Go to WINDOW on your calculator and change the x min and x max and the y min and y max

To zoom in on a certain area of the graph , press zoom and go to 2:zoom in

To return to standard settings, go to 6:zoom standard

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Changing style of a line

• You can change the line to a thick line, less then, greater than, or path , by moving to the left of the y= and pressing ENTER until you get to the setting you want.