UNIT 1B LESSON 2REVIEW OF LINEAR FUNCTIONS

Equations of Lines

The horizontal line through the point (2, 3) has equation

The vertical line through the point (2, 3) has equation

y = 3

x = 2

The vertical line through the point (a, b)has equation x = a since every x-coordinate on the line has the same value a.

Similarly, the horizontal line through (a, b) has equation y = b

Finding Equations of Vertical and Horizontal Lines

Vertical Line is x = – 3

Horizontal Line is y = 8

Unit 1B Lesson 2 Page 1Y1 = 2x + 7

x y- 30

y – intercept ( , )

m = 03

71

236

=

17

0 7

Slope y-intercept form

y = mx + b

slope y-intercept (0, b)

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.

y = – (A/B) x + C/B

By = – Ax + C

Ax + By = C

Analyzing and Graphing a General Linear Equation

Rearrange for y

Slope is

y-intercept is

Find the slope and y-intercept of the line

−𝟑−𝟑 𝒚=

−𝟐−𝟑 𝒙+

𝟏𝟓−𝟑

𝒚=𝟐𝟑 𝒙−𝟓

Unit 1B Lesson 2 Page 1EXAMPLESState the slopes and y-intercepts of the given linear functions.

y = 4x slope = m = _______ y -intercept ( , )3.

y = 3x – 5 slope = m = _______ y -intercept ( , )4.

)(xf 231

x= slope = m = _______ y -intercept ( , )5.

xxf 121)(

)(xf __________ slope = m = _______ y -intercept ( , )

6.

4

3

⅓

½ - ½ x -½

0 , 0

0 , - 5

0 , - 2

0 , ½

Find the slope and y-intercept of the following 3 lines

slope = m = _______ y-intercept

8. x + 2y = 3 slope = m = _______ y-intercept

9. 5x – 3y = – 4 slope = m = _______ y-intercept

𝟐𝟑 (𝟎 , −𝟓 )

𝟏𝟐 (𝟎 ,𝟑𝟐 )

𝟓𝟑 (𝟎 ,𝟒𝟑 )

b = 7

Example 10Find the equation in slope-intercept form for the line with slope and passes through the point

Step 1: Solve for b using the point

Step 2: Find the equation

(𝟎 ,𝟕)(−𝟑 ,𝟓)

Example 11Find the equation in slope-intercept form for the line parallel to and through the point (10, -1)

Step 2: Solve for b using the point

Step 3: Find the equation

Step 1: The slope of a parallel line will be

(𝟏𝟎 , −𝟏)

(𝟎 , −𝟓)

Example 12Write 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: is

Step 4: Graph on your calculator to check your work. Use a square window. Y1 = 3x – 4 Y2 = 3x + 5

(0, 5)

(0, – 4)

Example 13Write the equation for the line that is perpendicular to and passes through the point (10, – 1 )

Step 2: Solve for b using the point (10, – 1)

Step 3: The equation of the line ┴ to is

Step 1: The slope of a perpendicular line will be

Step 4: Graph on your calculator to check your work. Use a square window.

Y1 = Y2 = – x + 24

Example 14Write 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 .

Step 3: Find the equation of the line perpendicular to L: y = 3x – 4

Step 4: Graph on your calculator to check your work. Use a square window.

Y1 = 3x – 4 Y2

Step 2: Find b.

Example 15Find 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

Step 3: Find the equation

𝒎=

−𝟐−𝟖𝟕−(−𝟓)

=−𝟏𝟎𝟏𝟐 =−𝟓

𝟔

(7, – 2)

(– 4, 8)

Example 16Write the slope-intercept equation for the line through (– 2, –1) and (5, 4).

Slope = m =

Equation for the line is(5, 4)

(– 2, – 1)

Finish the 5 questions in Lesson #2