1. 3.1 Reading Graphs; Linear Equations in Two Variables
A linear equation in two variables can be put in the form: where A, B, and C are real numbers and A and B are not zero

2. 3.1 Reading Graphs; Linear Equations in Two Variables
Table of values: x y 6 2 3 4

3. 3.1 Reading Graphs; Linear Equations in Two Variables
Points: (2, 3) 2 is the x-coordinate, 3 is the y-coordinate
Quadrants:
II x<0 and y>0
I x>0 and y>0
III x<0 and y<0
IV x>0 and y<0

4. 3.2 Graphing Linear Equations in Two Variables
The graph of any linear equation in two variables is a straight line. Note: Two points determine a line.
Graphing a linear equation:
Plot 3 or more points (the third point is used as a check of your calculation)
Connect the points with a straight line.

5. 3.2 Graphing Linear Equations in Two Variables
Finding the x-intercept (where the line crosses the x-axis): let y=0 and solve for x
Finding the y-intercept (where the line crosses the y-axis): let x=0 and solve for y Note: the intercepts may be used to graph the line.

6. 3.2 Graphing Linear Equations in Two Variables
If y=k, then the graph is a horizontal line:
If x=k, then the graph is a vertical line:

7. 3.3 The Slope of a Line
The slope of a line through points (x1,y1) and (x2,y2) is given by the formula:
If the line is horizontal, m = 0.
If the line is vertical, m = undefined.

8. 3.3 The Slope of a Line A positive slope rises from left to right.
A negative slope falls from left to right.
Finding the slope of a line from its equation
Solve the equation for y.
The slope is given by the coefficient of x

9. 3.3 The Slope of a Line
Parallel lines (lines that do not intersect) have the same slope.
Perpendicular lines (lines that intersect to form a 90 angle) have slopes that are negative reciprocals of each other.
Horizontal lines and vertical lines are perpendicular to each other

10. 3.4 Equations of Lines General form: Ax + By = C
Slope-intercept form: y = mx + b (where m = slope and b = y-intercept)
Point-slope form: The line with slope m going through point (x1, y1) has the equation: y – y1 = m(x – x1)

11. 3.4 Equations of Lines
Example: Find the equation in slope-intercept form of a line passing through the point (-4,5) and perpendicular to the line 2x + 3y = 6 (solve for y to get slope of line) (take the negative reciprocal to get the  slope)

12. 3.4 Equations of Lines
Example (continued): Use the point-slope form with this slope and the point (-4,5) In slope intercept form: