This document discusses equations of lines, including linear functions and their standard, point-slope, and slope-intercept forms. It defines parallel and perpendicular lines based on their slopes. It provides examples of writing the equation of a line from its graph or from a point and slope. Key steps include calculating the slope, selecting a point, and writing the equation in the appropriate form.

1. Equations of Lines
Chapter 2 Graphs and Functions

2. Concepts & Objectives
 Linear Functions
 Write a linear function using either standard form,
point-slope form, or slope-intercept form
 Identify parallel and perpendicular lines

3. Linear Functions
 Reminder: A linear function can be written in one of the
following forms:
 Standard form: Ax + By = C, where A, B, C  , A 0,
and A, B, and C are relatively prime
 Point-slope form: y – y1 = mx – x1, where m   and
x1, y1 is a point on the graph
 Slope-intercept form: y = mx + b, where m, b  
 You should recall that in slope-intercept form, m is the
slope and b is the y-intercept (where the graph crosses
the y-axis).
 If A = 0, then the graph is a horizontal line at y = b.

4. Parallel and Perpendicular Lines
 Nonvertical lines are parallel iff (if and only if) they have
the same slope. Any two vertical lines are parallel.
 Two nonvertical lines are perpendicular iff the product
of their slopes is –1 (negative reciprocals). Vertical and
horizontal lines are perpendicular.
 Example: What is the slope of the line perpendicular
to y = –3x + 7?

5. Parallel and Perpendicular Lines
 Nonvertical lines are parallel iff (if and only if) they have
the same slope. Any two vertical lines are parallel.
 Two nonvertical lines are perpendicular iff the product
of their slopes is –1 (negative reciprocals). Vertical and
horizontal lines are perpendicular.
 Example: What is the slope of the line perpendicular
to y = –3x + 7?



1 1
3 3
or just flip –3 and change the sign:


3 1
1 3

6. Writing the Equation of a Line
 From a graph:
 Calculate the slope
 Select a point on the graph. If the y-intercept is
available, use that by preference.
 Write the equation in either point-slope form or
slope-intercept form.

7. Writing the Equation of a Line
 Ex.: Write the equation of the graph:

8. Writing the Equation of a Line
 Ex.: Write the equation of the graph:
 The y-intercept (b) is –1.
 The slope is up 2, over 3 or .
2
3

9. Writing the Equation of a Line
 Ex.: Write the equation of the graph:
 The y-intercept is –1.
 The slope is up 2, over 3 or .
2
3
 
2
1
3
y x

10. Writing the Equation of a Line
 Ex.: Write the equation of the graph:
 The y-intercept is –1.
 The slope is up 2, over 3 or .
 To convert to standard form:
2
3
 
2
1
3
y x
   
2
1
3
x y
  
      
 
2
3 3 1
3
x y   2 3 3x y

11. Writing the Equation of a Line
 From a point and a slope:
 Plug into the point-slope form and transform it into
the requested form (slope-intercept or standard) if
necessary.
 From two points:
 Calculate the slope, and pick one point to plug into
the point-slope form.

12. Writing the Equation of a Line
 Example: Write the equation in slope-intercept form for
the line that contains the point (2, –7) and has slope –3.

13. Writing the Equation of a Line
 Example: Write the equation in slope-intercept form for
the line that contains the point (2, –7) and has slope –3.
y – (–7) = –3(x – 2)
y + 7 = –3x + 6
y = –3x – 1

14. Classwork
 2.5 Assignment (College Algebra)
 Page 242: 6-20 (even), page 226: 36-50 (even, omit
44), page 215: 74-86 (even)
 2.5 Classwork Check
 Quiz 2.4