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