Write the equation of a line

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
⚫ 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
⚫ Find 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 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 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 solve for y if
requested.
⚫ From two points:
⚫ Calculate the slope, and pick one point to plug into
the point-slope form.
⚫ Alternatively, you can plug the slope and the point’s x
and y values into the slope-intercept form, solve for b,
and re-write the equation.

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.
⚫ Method #1: y – (–7) = –3(x – 2)
y + 7 = –3x + 6
y = –3x – 1
⚫ Method #2: –7 = –3(2) + b
–7 = –6 + b
–1 = b  y = –3x – 1

14. Classwork
⚫ College Algebra
⚫ Page 242: 6-20 (even), page 226: 36-42 (even), page
164: 44-56 (even)