Equations of Lines

1. Section 2.4
Writing Equations of Lines
 Point-Slope Form (y – y1) = m(x – x1)
 Slope-Intercept Form y = mx + b
 Using Slope to Help Graphing
 Parallel & Perpendicular Lines
 Curve Fitting (skip)

2. Forms of Lines
 Point Slope Form of a line
( ) 1 1 y  y  m x  x
 Example: A line with slope -2 goes thru (3,-5)
 y - -5 = -2(x – 3)
 y + 5 = -2(x – 3)
 Slope-Intercept Form of a line
y  mx b
 Example: A line with slope -2 has y-intercept (0,3)
 y = -2x + 3

3. Practice
 Write y + 2 = ⅓(x + 3) in slope–intercept form
 Write the equation of the line that has slope 2
and passes through the point (3, 1)
 Write the equation of the line with m=7,
passing through the origin

4. Graphing a Line from y = mx +b
(start at the y-intercept, use the slope)
For 4x – 3y = 6
1. Rearrange into y = mx + b
3y = 4x – 6
y = 4/3x – 2
m = 4/3 y-int = (0,-2)
2. Graph the point (0,-2)
3. Plot a 2nd point using
slope (right 3, up 4)

5. Parallel and Perpendicular Lines
 Parallel lines have the same slope.
 m1 = m2
 Example: y = 9x – 2 and y = 9x + 5
 Perpendicular lines have slopes that are
negative reciprocals of each other.
 m1 = -1/m2
 Example: y = 9x – 2 and y = -x/9 – 3

6. Practice
 Are the following parallel, perpendicular or neither?
13
1
y  4x 13 y  x 
4
 Write the equation of the line that passes through
(-6,3) and is parallel to the line y + 3x = -12

7. What Next?
 Present Section 2.5
An Introduction to Functions