1. Linear Representation and Equations of Lines
Unit 2.2
Linear Representation and
Equations of Lines

2. Linear Representations
Linear Data can be represented in a variety of ways:
x-y tables
Graphs
Equations
Verbal representation

3. Slope-Intercept Form of a Line
y = mx + b
Y-intercept of line
Slope of line
x and y are points (x,y) on the line

4. Practice Problems
Identify the slope (m) and y-intercept (b) of the following lines:
y = ½ x – 4
y = -3x + 5
y = 6 – 2x
y = -2/3x + 10
5. y = x

5. Writing Linear Equation from Slope and y-intercept
If we know the slope (m) and y-intercept (b), we can write the equation of a line.
Examples:
m = ¾ , b= Equation: y = ¾ x – 6
m = -2, b = Equation: y = -2x + 3
m = 0, b = Equation: y = (0)x + 5 or
y = 5

6. Practice Problems Write the equations for the following lines:
1. m = 3, b = -4
2. m = -1/2, b=2
3. m = 6, b = 0
4. m = 2/5, b = -2
5. m = 9/5, b = 32

7. Write the equation of the line in slope-intercept form for the following graph:
b =
Equation:

8. Writing Equation from the slope and one point
If we know the slope of a line and one point on the line, we can find the y-intercept by doing the following:
Replace m with the slope given in the problem
Use the point we know to replace x and y
Solve for b

9. Example 1:
Find the equation of the line with a slope of 2 that passes through point (1, 6).
m = 2, x = 1, y = 6
Use the general equation: y = mx + b to find b
6 = 2(1) + b
6 = 2 + b
4 = b Equation of line: y = 2x + 4

10. Example 2:
Find the equation of the line with a slope of ½ that passes through (4, 8).
m = ½ , x = 4, y = 8
y = mx + b
8 = ½(4) + b
8 = 2 + b
6 = b Equation of line: y = ½ x + 6

11. Practice Problems
Write the equation of the line with the following information:
1. m = -3, contains (1, -12)
2. m = 4, contains (-1, 6)
3. m = -1, contains (0, 3)
4. m = 2/3, contains (6, 9)

12. Writing Equation from Two Points
We can also write the equation if we know two points on the line:
Find the slope of the line passing through the two points (this is m)
Find the y-intercept by solving for b using the slope and one point on the line
Put m and b into the general equation
y = mx + b

13. Example:
Find the equation of the line passing through (1,4) and (2,2).
1. Find slope: m = = -2
2. Find b: y = mx + b m = -2, x = 1, y = 4
y = mx + b
4 = -2(1) + b
4 = -2 + b
6 = b
3. Equation: y = -2x + 6

14. Practice Problem
Find the equation of the line passing through (-2,5) and ( 1,2)
m =
b =
Equation:

15. Example 1: Joe puts $50 in a savings account and saves $15 a week
Example 1: Joe puts $50 in a savings account and saves $15 a week. Table Equation Graph Week Money

16. Example 2: Cost of fixing a furnace
Table: Equation: Graph:
Hours Cost
$50
$75
$100
$125
$150
Verbal:

17. Example 3:
Table Equation
X | Y

18. Standard Form of a Line The standard form of a line is ax + by = c
where a, b, are integers, c is real number and
x and y are points on the line
The standard form of a line is often used to find x- and y-intercepts.