1. Graphing linear equations
Lesson 13
Graphing linear equations

2. 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.

3. 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.

4. 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

5. 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

6. 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

7. Moving from point to point using the slope
Positive slope up or down
right left
Negative slope up or down
left right

8. 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
3) calculate the slope of the lines that contain the following points:
(-3,5)(5,6) (0,4)(-2,0) (-4,3)(8,3)

9. Lab 3 Calculating 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

10. 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

11. 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

12. 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.