1. Equations of lines

2. Given the slope and y-intercept.
Use slope-intercept formula.
Substitute the slope for m.
Substitute the y-intercept for b.
Ex. Write the equation of a line that has a y-intercept of -3 and a slope of ½.

3. Given the slope and a point.
Use point-slope formula.
Substitute the slope for m.
Substitute the point for (x1, y1).
Ex. Write the equation of a line that has a slope of 2 and passes through the point (-1, -3).

4. Given two points.
Use the slope formula.
Find the slope.
Use point-slope formula.
Substitute the slope for m.
Substitute one of the given points for (x1, y1).
Ex. Write the equation of a line passes through the points (0, -3) and (4, 5).

5. D: {2}, R: {all real numbers}
Vertical Lines
Have an undefined slope.
Equation: x = #
Domain is a single x-value.
Range is all real numbers.
Example
x = 2
D: {2}, R: {all real numbers}

6. D: {all real numbers}, R: {2}
Horizontal Lines
Have a slope of zero.
Equation: y = #
Domain is all real numbers.
Range is a single y-value.
Example
y = 2
D: {all real numbers}, R: {2}

7. x-intercept Point where a line crosses the x-axis. (#, 0)
Find by setting y = 0 and solving for x.

8. y-intercept Point where a line crosses the y-axis. (0, #)
Find by setting x = 0 and solving for y.

9. The graph has a slope of -3 and a y-intercept of 4.
Describing a graph
Describe a graph of a linear equation using the slope and y-intercept.
First write the equation in slope-intercept form.
Ex. 3x + y = 4
y = -3x + 4
The graph has a slope of -3 and a y-intercept of 4.

10. Parallel Lines Ex. y = -3x + 4 and y = -3x – 3 Same slope
Different y-intercepts
Parallel lines will NEVER intersect.
Ex. y = -3x + 4 and y = -3x – 3

11. Perpendicular Lines Ex. y = -3x + 4 and y = (1/3)x – 3
Slopes are opposite reciprocals
Different y-intercepts
Perpendicular lines form 90 degree angles at their intersection.
Ex. y = -3x + 4 and y = (1/3)x – 3