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UNIT 1B LESSON 2
REVIEW 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
(𝟐 ,𝟓 )
(𝟐 ,𝟑 )
(𝟐 ,𝟎 )(𝟐 ,−𝟐 )
(−𝟏 ,𝟑 ) (𝟒 ,𝟑 )(𝟎 ,𝟑 ) (𝟐 ,𝟑 )
Finding Equations of Vertical and Horizontal Lines
Vertical Line is x = – 3
Horizontal Line is y = 8
EXAMPLE 1 Write the equations of the vertical and horizontal lines through the point
(−𝟑 ,𝟖 )
Y1 = 2x + 7
x Y = 2x + 7
y – intercept ( , )
𝟐 (−𝟑 )+𝟕=𝟏𝟐 (𝟎 )+𝟕=𝟕
𝟎 𝟕
Slope y-intercept form y = mx + b
slope y-intercept (0, b)
EXAMPLE 2: Reviewing Slope-Intercept Form of Linear Functions
𝒎=𝒓𝒊𝒔𝒆𝒓𝒖𝒏
=𝒚𝟐− 𝒚𝟏
𝒙𝟐− 𝒙𝟏
𝒎=𝟏−𝟕
−𝟑−𝟎=
−𝟔−𝟑
=𝟐
(𝟎 ,𝟕)
(−𝟑 ,𝟏)
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 23
1x= slope = m = _______ y -intercept ( , )6.
xxf 12
1)(
slope = m = _______ y -intercept ( , )
6.
4
3
⅓
𝒇 (𝒙 )=𝟏𝟐
−𝟏𝟐𝒙
0 , 0
0
0 ,
0 ,
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=𝟐𝟑𝒙−𝟓
𝟐
𝟑𝟒
𝟔
Example 7
Unit 1B Lesson 2 Page 1EXAMPLESState the slopes and y-intercepts of the given linear functions.
x + 2y = 3 slope = m = _______ y -intercept ( , )8.−𝟏𝟐
𝟐 𝒚=−𝒙+𝟑
0 , 3/2
𝒚=−𝟏𝟐𝒙+
𝟑𝟐
slope = m = _______ y -intercept ( , )9.
−𝟑 𝒚=−𝟓 𝒙−𝟒
𝒚=𝟓𝟑𝒙+
𝟒𝟑
𝟓𝟑 0 , 4/3
𝟓=𝟐𝟑
(−𝟑 )+𝒃
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)
𝒚=𝒎𝒙+𝒃
b = 7
𝟓=−𝟐+𝒃
𝒎=𝟐𝟑
−𝟏=𝟐𝟓
(𝟏𝟎 )+𝒃
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
𝒃=−𝟓−𝟏=𝟒+𝒃
𝒚=𝒎𝒙+𝒃
(𝟎 ,−𝟓)
(𝟎 ,𝟐)
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)
𝒃=𝟓𝟐=−𝟑+𝒃𝟐=𝟑(−𝟏)+𝒃
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 negative reciprocal
Step 4: Graph on your calculator to check your work. Use a square window.
Y1 = Y2 = – x + 24
𝒃=𝟐𝟒−𝟏=−𝟐𝟓+𝒃
−𝟓𝟓
𝟐𝟐
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 .
𝟐=−𝟏𝟑
(−𝟏)+𝒃
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.
𝒃=𝟓𝟑𝟐=
𝟏𝟑
+𝒃𝟔𝟑
=𝟏𝟑
+𝒃
−𝟐=−𝟓𝟔
(𝟕)+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
𝟖=−𝟓𝟔
(−𝟓)+𝒃𝒎=−𝟐−𝟖𝟕−(−𝟓)
=−𝟏𝟎𝟏𝟐
=−𝟓𝟔
(7, – 2)
(– 5, 8)
𝒃=𝟐𝟑𝟔
−𝟏𝟐𝟔
=−𝟑𝟓𝟔
+𝒃
𝒃=𝟐𝟑𝟔
𝟒𝟖𝟔
=𝟐𝟓𝟔
+𝒃
EXAMPLE 16Write the slope-intercept equation for the line through (– 2, –1) and (5, 4).
Slope = m =
–𝟏=𝟓𝟕
(–𝟐)+𝒃
Equation for the line is
(5, 4)(– 2, – 1)
𝒃=𝟑𝟕
−𝟕𝟕
=−𝟏𝟎𝟕
+𝒃
Finish the 5 questions in Lesson #2