1. U1B L2 Reviewing Linear Functions
UNIT 1B LESSON 2
REVIEW OF LINEAR FUNCTIONS

2. U1B L2 Reviewing Linear Functions
Equations of Lines
The vertical line through the point (a, b)
has equation x = a since every x-coordinate on the line has the same value a.
𝟐,𝟓
−𝟏,𝟑
𝟎,𝟑
𝟐,𝟑
𝟒,𝟑
𝟐,𝟑
Similarly, the horizontal line through (a, b) has equation y = b
𝟐,𝟎
The horizontal line through the point (2, 3) has equation
𝟐,−𝟐
y = 3
The vertical line through the point (2, 3) has equation
x = 2

3. Finding Equations of Vertical and Horizontal Lines
U1B L2 Reviewing Linear Functions
Finding Equations of Vertical and Horizontal Lines
EXAMPLE 1
Write the equations of the vertical and horizontal lines
through the point −𝟑, 𝟖
Horizontal Line is y = 8
−𝟑, 𝟖
Vertical Line is x = – 3

4. U1B L2 Reviewing Linear Functions
EXAMPLE 2: Reviewing Slope-Intercept Form of Linear Functions
Y1 = 2x + 7
Slope y-intercept form
y = mx + b
slope y-intercept (0, b) x
Y = 2x + 7 −3
𝟐 −𝟑 +𝟕=𝟏
𝟐 𝟎 +𝟕=𝟕
y – intercept ( , ) 𝟎 𝟕
(𝟎,𝟕)
𝒎= 𝒓𝒊𝒔𝒆 𝒓𝒖𝒏 = 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
𝒎= 𝟏−𝟕 −𝟑−𝟎 = −𝟔 −𝟑 =𝟐
(−𝟑,𝟏)

5. U1B L2 Reviewing Linear Functions
Unit 1B Lesson 2 Page 1
EXAMPLES
State the slopes and y-intercepts of the given linear functions.
y = 4x slope = m = _______ y -intercept ( , ) 3. 4
0 , 0
y = 3x – slope = m = _______ y -intercept ( , ) 4. 3
0 , −𝟓 =
slope = m = _______ y -intercept ( , ) 6. ⅓
0 , −𝟐
slope = m = _______ y -intercept ( , ) 6.
− 𝟏 𝟐
0 , ½
𝒇 𝒙 = 𝟏 𝟐 − 𝟏 𝟐 𝒙

6. General Linear Equation
U1B L2 Reviewing Linear Functions
General Linear Equation
Although the general linear form helps in the quick identification of lines, the slope-intercept form is the one to enter into a calculator for graphing.
Ax + By = C
By = – Ax + C
y = – (A/B) x + C/B

7. Analyzing and Graphing a General Linear Equation
U1B L2 Reviewing Linear Functions
Analyzing and Graphing a General Linear Equation
Example 7
Find the slope and y-intercept of the line 2𝑥−3𝑦=15
Rearrange for y
−𝟑𝒚 = −𝟐𝒙 + 𝟏𝟓
−𝟑 −𝟑 𝒚 = −𝟐 −𝟑 𝒙+ 𝟏𝟓 −𝟑 𝟔
𝒚= 𝟐 𝟑 𝒙−𝟓 𝟑 𝟒 𝟐
y-intercept is (𝟎, −𝟓)
Slope is 𝟐 𝟑

8. U1B L2 Reviewing Linear Functions
Unit 1B Lesson 2 Page 1
EXAMPLES
State the slopes and y-intercepts of the given linear functions.
− 𝟏 𝟐
x + 2y = 3 slope = m = _______ y -intercept ( , ) 8.
0 , 3/2
𝟐𝒚 = −𝒙 +𝟑
𝒚 =− 𝟏 𝟐 𝒙 + 𝟑 𝟐
𝟓 𝟑
5𝑥−3𝑦 =−4 slope = m = _______ y -intercept ( , ) 9.
0 , 4/3
−𝟑𝒚 = −𝟓𝒙 −𝟒
𝒚 = 𝟓 𝟑 𝒙 + 𝟒 𝟑

9. U1B L2 Reviewing Linear Functions
EXAMPLE 10
Find the equation in slope-intercept form for the line with slope 𝟐 𝟑 and passes through the point (−𝟑, 𝟓)
𝒎= 𝟐 𝟑
Step 1: Solve for b using the point (−𝟑, 𝟓)
𝒚=𝒎𝒙+𝒃
𝟓= 𝟐 𝟑 −𝟑 +𝒃
𝟓=−𝟐+𝒃
(𝟎, 𝟕)
(−𝟑, 𝟓)
b = 7
Step 2: Find the equation
𝒚= 𝟐 𝟑 𝒙+𝟕

10. U1B L2 Reviewing Linear Functions
EXAMPLE 11
Find the equation in slope-intercept form for the line parallel to 𝒚 = 𝟐 𝟓 𝒙 + 𝟐
and through the point (10, -1)
Step 1: The slope of a parallel line will be 𝟐 𝟓
Step 2: Solve for b using the point (𝟏𝟎, −𝟏)
𝒚=𝒎𝒙+𝒃
(𝟎, 𝟐)
−𝟏= 𝟐 𝟓 𝟏𝟎 +𝒃
−𝟏=𝟒+𝒃
𝒃 = −𝟓
Step 3: Find the equation
(𝟎, −𝟓)
𝒚 = 𝟐 𝟓 𝒙 – 𝟓

11. U1B L2 Reviewing Linear Functions
EXAMPLE 12
Write the equation for the line through the point (– 1 , 2) that is
parallel to the line L: y = 3x – 4
Step 1: Slope of L is 3 so slope of any parallel line is also 3.
Step 2: Find b.
Step 3: The equation of the line
parallel to
L: 𝒚 = 𝟑𝒙 – 𝟒 is 𝒚 = 𝟑𝒙 + 𝟓
𝟐 = 𝟑(−𝟏) + 𝒃
𝟐 =−𝟑+𝒃
𝒃 = 𝟓
Step 4: Graph on your calculator to check your work.
Use a square window.
Y1 = 3x – 4
Y2 = 3x + 5
(0, 5)
(0, – 4)

12. U1B L2 Reviewing Linear Functions
EXAMPLE 13
Write the equation for the line that is perpendicular to
𝒚 = 𝟐 𝟓 𝒙 + 𝟐 and passes through the point (10, – 1 )
Step 1: The slope of a perpendicular line will be – 𝟓 𝟐 negative reciprocal
Step 2: Solve for b using the point (10, – 1)
−𝟏 = – 𝟓 𝟐 (𝟏𝟎) + 𝒃
Step 3: The equation of the line ┴ to 𝒚 = 𝟐 𝟓 𝒙 + 𝟐 is 𝒚 = – 𝟓 𝟐 𝒙 + 𝟐𝟒
−𝟏=−𝟐𝟓+𝒃
𝒃 = 𝟐𝟒
Step 4: Graph on your calculator to check your work. Use a square window.
Y1 = 𝟐 𝟓 𝒙 + 𝟐
Y2 = – 𝟓 𝟐 x + 24 𝟐 𝟐 −𝟓 𝟓

13. U1B L2 Reviewing Linear Functions
EXAMPLE 14
Write the equation for the line through the point (– 1, 2) that is
perpendicular to the line L: y = 3x – 4
Step 1: Slope of L is 3 so slope of any perpendicular line is − 𝟏 𝟑 .
Step 2: Find b.
𝟐 =− 𝟏 𝟑 (−𝟏) + 𝒃
𝒃 = 𝟓 𝟑
𝟐 = 𝟏 𝟑 + 𝒃
𝟔 𝟑 = 𝟏 𝟑 + 𝒃
Step 3: Find the equation of the line perpendicular to L: y = 3x – 4
𝒚 =− 𝟏 𝟑 𝒙 + 𝟓 𝟑
Step 4: Graph on your calculator
to check your work.
Use a square window.
Y1 = 3x – 4
Y2 =− 𝟏 𝟑 𝒙 + 𝟓 𝟑

14. U1B L2 Reviewing Linear Functions
EXAMPLE 15
Find the equation in slope-intercept form for the line that passes
through the points (7, −2) and (−5, 8).
Step 1: Find the slope
Step 2: Solve for b using either point
𝒎= −𝟐−𝟖 𝟕−(−𝟓) = −𝟏𝟎 𝟏𝟐 =− 𝟓 𝟔
−𝟐 =− 𝟓 𝟔 (𝟕) + 𝒃
𝟖 =− 𝟓 𝟔 (− 𝟓) + 𝒃
− 𝟏𝟐 𝟔 =− 𝟑𝟓 𝟔 + 𝒃
𝟒𝟖 𝟔 = 𝟐𝟓 𝟔 + 𝒃
𝒃 = 𝟐𝟑 𝟔
𝒃 = 𝟐𝟑 𝟔
Step 3: Find the equation
(– 5, 8)
𝒚 =− 𝟓 𝟔 𝒙 + 𝟐𝟑 𝟔
(7, – 2)

15. U1B L2 Reviewing Linear Functions
EXAMPLE 16
Write the slope-intercept equation for the line through
(– 2, –1) and (5, 4).
Slope = m = −𝟏−𝟒 −𝟐−𝟓 = −𝟓 −𝟕 = 𝟓 𝟕
–𝟏= 𝟓 𝟕 (–𝟐) + 𝒃
−𝟕 𝟕 = −𝟏𝟎 𝟕 + 𝒃
𝒃 = 𝟑 𝟕
(5, 4)
(– 2, – 1)
Equation for the line is
𝒚 = 𝟓 𝟕 𝒙 + 𝟑 𝟕

16. U1B L2 Reviewing Linear Functions
Finish the 5 questions in Lesson #2