GEOMETRY
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name______________________
M4
Period: ______ Date: ________________
Lesson 3: Writing the Equations of Lines
Learning Target
 I can write the equations of lines in slope- intercept and slope-point form when two points are given, a
graph is given, and the slope and one point is given
Opening Exercise: Find the slope and 𝑦 – intercept of each equation:
a) 𝑦 = 3𝑥 − 9
b) 2𝑦 − 6 = 3𝑥
c) −2𝑦 = 6(5 − 3𝑥)
Formulas/Equations you MUST know for Geometry
Slope (rate of change):
Δ𝑦
𝑦 −𝑦
𝑚 = Δ𝑥 = 𝑥2 −𝑥1
2
Slope-Intercept form of a linear function:
Standard form of a linear function:
1
𝑦 = 𝑚𝑥 + 𝑏
𝐴𝑥 + 𝐵𝑦 = 𝐶
Vertical lines: 𝒙 = 𝒂 𝒏𝒖𝒎𝒃𝒆𝒓, have undefined slope (VUX).
Horizontal lines: 𝒚 = 𝒂 𝒏𝒖𝒎𝒃𝒆𝒓, have zero slope (HOY).
We will learn the point–slope form of a linear function: ___________________________________
A. Finding the Slope when Two Points are Given
Example 1. Find the slope of the line that passes through the points (3, 2) and (−9, 6).
𝑚=
Δ𝑦 𝑦2 − 𝑦1 𝑦2 − 𝑦1
=
=
=
Δ𝑥 𝑥2 − 𝑥1 𝑥2 − 𝑥1
Example 2. Find the slope of the line that passes through the points (−5, −7) and (0, 10).
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name______________________
B. Writing Equation of a Line from Two Points
Lesson 3
M4
Period: ______ Date: ________________
http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-215s.html
Example 3. A line passes through the points (3,5) and (7, −3) , write the equation of the line in
(a) slope-intercept form: 𝑦 = 𝑚𝑥 + 𝑏
(b) point-slope form: 𝑦 – 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Steps
1. Find the slope using the slope formula
2. Substitute on the 𝑦 = 𝑚𝑥 + 𝑏 one point
and the 𝑚
3. Solve for 𝑏
4. Write the equation of the line 𝑦 = 𝑚𝑥 + 𝑏
Steps
1. Find the slope using the slope formula
2. Use one point and the slope 𝒎 to substitute on
the point-slope form: 𝑦 – 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Example 4. Write the equation of a line that passes through the points (2, 4) and (−3, −6) in:
a) point-slope form:
b) slope–intercept form:
GEOMETRY
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name______________________
C. Write the Equation of a Line from the Graph
M4
Period: ______ Date: ________________
Example 5. For the graphs below write the equation of the lines either in
𝑦 = 𝑚𝑥 + 𝑏
or
𝑦 – 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Steps
 Find the slope using two points on the graph or use rise over run
 Identify or find the y-intercept
 Write the equation in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) or use the slope and a point on the line to
write the equation in point-slope form 𝑦 – 𝑦1 = 𝑚(𝑥 − 𝑥1 ).
a.
b.
slope–intercept form: _______________________
slope–intercept form: _______________________
point-slope form: ___________________________
point-slope form: ___________________________
D. Write the Equation Given Slope and One Point
Write your answer in either point-slope form or slope-intercept form
Example 6. 𝑚 = −3; (−6, 2)
GEOMETRY
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name______________________
M4
Period: ______ Date: ________________
Lesson 3: Writing the Equations of Lines
Classwork
1) Given 𝑨(𝟓, −𝟕) and 𝑩(𝟖, 𝟐), find an equation for the line through 𝑨 𝒂𝒏𝒅 𝑩 (Write your answer in either
point-slope form or slope-intercept form)
2) Write the Equation Given Two Points (Write your answer in either point-slope form or slope-intercept form)
a. (−1,0), (1,2)
b. (−6,6), (3,3)
3) Write the Equation given the slope and one point (Write your answer in either point-slope form or slopeintercept form)
2
a. 𝑚 = − 5 ; (4,0)
b. 𝑚 = 0; (2, −4)
4) Write the equation of the line in either 𝑦 = 𝑚𝑥 + 𝑏 or 𝑦 – 𝑦1 = 𝑚(𝑥 − 𝑥1 )
a.
b.
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 3
M4
Name______________________
Period: ______ Date: ________________
5) Graph each equation. Remember to label the graph appropriately!
a.
2𝑦 − 4𝑥 = 0
b. 𝟑y + 6 = 2x
6) Find the slope and 𝑦-intercept of the given equation.
(a) −3x + 2y = 6
***(b) 𝐴𝑥 + 𝐵𝑦 = 𝐶
7) A triangle in the coordinate plane has vertices 𝑨(𝟎, 𝟏𝟎), 𝑩(−𝟖, 𝟖), and 𝑪(−𝟑, 𝟓). Find the following:
Slope of segment ̅̅̅̅
𝐴𝐵 __________
̅̅̅̅ _____________________________
Equation of segment 𝐴𝐵
̅̅̅̅ __________
Slope of segment 𝐵𝐶
̅̅̅̅ _____________________________
Equation of segment 𝐵𝐶
̅̅̅̅ __________
Slope of segment 𝐶𝐴
Equation of segment ̅̅̅̅
𝐶𝐴 ______________________________
GEOMETRY
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
Name______________________
Period: ______ Date: ________________
8) Given points 𝑆(2, 4), 𝑇(7, 6), 𝑈(−3, −4), and 𝑉(−1, −9):
̅̅̅ and 𝑈𝑉
̅̅̅̅
Write the equations of segments ̅𝑆𝑇
𝑻(𝟕, 𝟔)
𝑺(𝟐, 𝟒)
𝑼(−𝟑, −𝟒)
𝑽(−𝟏, −𝟗)
9) Write the equation of the line with a slope 𝑚 = 2 and that passes through a point (8, 4)
10) Write the equation of a line in point-slope form that passes through two points (1, 5) 𝑎𝑛𝑑 (4, −1)