Algebra 1
Standard 9
Writing Equations of Lines
Categories
• Equations from Graphs
• Equations from Data
• Equations from Tables
• Equations of Horizontal & Vertical Lines
Summative Assessment Date:
Monday, January 14th
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Standard: Writing Equations of Lines
Equations from Graphs
Learning Target
1
2
3
4
6
7
8
Class
Check
Do I need
more practice?
HW
Results
Class
Check
Do I need
more practice?
HW
Results
Class
Check
Do I need
more practice?
HW
Results
Class
Check
Do I need
more practice?
I can find the rate of change of a graph.
I can write an equation of a graph using point-slope.
I can write an equation of a graph using point-slope.
I can write an equation of a graph in slope-intercept
form.
Equations from Data
Learning Target
5
HW
Results
I can write an equation when given a point and a slope
in both forms
I can write an equation when given a y-intercept and a
slope in both forms
I can find the rate of change between two points.
I can write an equation when given two points in both
forms
Equations from Tables
Learning Target
9
10
I can determine the rate of change from a table.
I can write an equation from a table in both forms
Horizontal & Vertical
Learning Target
11
12
13
I can write an equation of a horizontal or vertical line
from a graph.
I can write an equation of a horizontal or vertical line
from a table.
I can write an equation of a horizontal or vertical line
from data.
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Writing Equations of Lines – DAY 1
Notes – Point-Slope Form (p3-4)
Review – Graph the two given linear equations.
A.
B. y = −
y = 2x − 3
1
( x + 2) + 1
3
KEY CONCEPT: What are the two things you used from the equations to make their graphs?
1.
2.
Writing equations of lines can be done in many different forms.
Today we are looking at Point-Slope Form.
Write down point-slope form here:
Example 1
Write the equation of the line that has a slope of -2
and passes through the point (1, -5). Then graph the line.
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Example 2
Write the equation of the line that has a slope of
1
4
and passes through the point (-4, 0). Then graph the line.
Example 3
Write an equation of the line
that is graphed below.
Example 4
Write an equation of the line
that is graphed below.
YOUR TURN
1. Write the equation of a line that has a slope of -6 and passes through the point (0, 2).
2. Write the equation of a line that has a slope of 1 and passes through the point (-3 ,-4).
3. Write the equation of the line that is graphed to the right.
Page | 4
Writing Equations of Lines – DAY 1
Homework – Point-Slope Form (p5-6)
Point-Slope Form
y = m ( x − x1 ) + y1
or
y = m ( x − h) + k
For numbers 1-6, WRITE THE EQUATION using the given information and then graph the line.
1.
slope is 2, passes through (4, -3)
2.
Equation:
3.
slope is
2
, passes through (-1, 6)
3
Equation:
4.
Equation:
5.
slope is 0, passes through (4, -2)
Equation:
slope is -1, passes through (0,0)
5
slope is − , passes through (-2, -1)
2
Equation:
6.
slope is -3, passes through (2, 9)
Equation:
For numbers 7-9, write an equation of the given graph.
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7.
8.
9.
Review from First Semester – Graph Absolute Value Functions
For numbers 10 and 11, graph the given absolute value equation.
10. y = −
1
x − 5 +1
2
11. y = 2 x + 6
Writing Equations of Lines – DAY 2
Page | 6
Notes – Given Two Points (p7-8)
RECALL:
POINT-SLOPE FORM OF A LINE
y = a ( x − h) + k
Or
RECALL:
y = m ( x − x1 ) + y1
SLOPE/ RATE OF CHANGE / a / m
For two points ( x1 , y1 ) and ( x2 , y2 ) : slope = r.o.c. = a = m =
y2 − y1
x2 − x1
Note: always simplify as an improper fraction. Do NOT give as a decimal.
EX 1: Write the equation of the line that goes through the following points: (3, -8) and (-5, 4)
a) What do we need?
b) How do we get it?
c) Then what do we do?
d) Answer: ______________________
EX 2:
(YOU TRY) Write the equation of the line that goes through the following points: (9, -6) and (-5, 12)
EX 3:
(YOU TRY) Write the equation of the line that goes through the following points: (-8, 1) and (-20, -1)
EX 4: Write the equation of the line that represents the data from the given table.
Page | 7
Input
Output
-4
-11
-2
-7
-1
-5
3
3
6
9
EX 5: (YOU TRY) Write the equation of the line that represents the data from the given table.
x
f(x)
-6
8
0
6
3
5
12
2
15
1
EX 6: Write an equation for a line of best fit that represents the data from the scatterplot.
A scatterplot is a graph of plotted data points.
1) You must first draw a line of best fit:
a) it should follow the shape of the points
b) it should have about as many points above and below it
2) Pick two points on the line of best fit (they do NOT have
to be actual data points)
3) Use the two points to write the equation of the best fit line
EX 7:
(YOU TRY) Write an equation for a line of best fit that represents the data from a scatterplot.
Page | 8
Writing Equations of Lines – DAY 2
Homework – Given Two Points (p9)
Write the equation of the line that goes through the following points.
1. (-5, 3) and (-15, 7)
2. (1, -3) and (-4, -18)
Write the equation of the line that represents the data from the given tables.
3.
4.
Write the equation of the lines graphed below.
7
7
y
6
5.
6.
5
y
6
5
4
4
3
3
2
2
1
1
x
x
−7
−6
−5
−4
−3
−2
−1
−1
1
2
3
4
5
6
−7
7
−6
−5
−4
−3
−2
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
−7
−7
Find the slope two different ways.
1)
2)
1
2
3
4
5
6
7
Find the slope two different ways.
1)
2)
Equation: _______________________
Equation: _______________________
Write an equation for a line of best fit that represents the data from a scatterplot.
7.
8.
Equation: _______________________
Equation: _______________________
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Writing Equations of Lines – DAY 3
Notes – Slope-Intercept Form (p10-11)
Simplifying
5
1
3) − x + 2 − 5
3
9
1) 5 x − 4 − 9
2) − 3.4 x − 5.4 + 10.2
4) 5( x − 4)
5) − 3( x − 5) + 10
5
6) − ( x + 4) − 5
2
1
7) − ( x + 2) − 5
3
8) − ( x − 4) + 5
9)
5
( x + 5) + 1
6
Graph the line y = −3( x − 1) + 1
What is the y-intercept?
Simplify the equation y = −3( x − 1) + 1 .
So when an equation is in y = mx + b form, we call it _______________________________
because m is the ___________ and b is the __________________.
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Each problem models a linear function. Write the equation in SLOPE–INTERCEPT FORM.
Page | 11
Writing Equations of Lines – DAY 3
Homework – Slope-Intercept Form (p12-13)
For #s 1-6, convert each POINT-SLOPE equation to SLOPE-INTERCEPT.
1. y = −6( x + 2) − 4
2. y = −6( x − 8)
4.
1
y = ( x − 9) + 2
3
2
5. y = ( x + 7) − 3
3
3. y = − ( x + 4) − 9
6.
5
y = − ( x − 5) + 4
6
Write each equation in SLOPE-INTERCEPT FORM.
7) goes through (0,3) and has a slope of −
9) goes through (2, -4) and (-3, 2)
1
3
8) goes through (-1, 3) and has a slope of 6
10) goes through (0, 5) and (6, 3)
Page | 12
11)
12)
13)
14)
y
y
4
4
3
3
2
2
1
1
x
−4
15)
−3
−2
−1
1
2
3
x
4
−4
−3
−2
−1
1
−1
−1
−2
−2
−3
−3
−4
−4
2
3
4
16)
Page | 13
Writing Equations of Lines – DAY 4
Notes – Slope-Intercept Form (p14-16)
Example 1:
Slope:
Point-slope form:
Final equation:
Example 2:
A)
Rate of change:
B)
Rate of change:
Horizontal Lines
Vertical Lines
Equation: ____________________
Equation: ____________________
Rate of Change:_______________
Rate of Change:_______________
Example 3: Write the equations from example 2.
A) ____________________________
B) ____________________________
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Example 4: Write the equations of the given graph.
1)
2)
Equation:
Equation:
3)
4)
Equation:
Equation:
Example 5:
Example 6:
Rate of change:
Rate of change:
Vertical or horizontal?
Vertical or horizontal?
Equation:
Equation:
Page | 15
Example 7: Write the equation of the line through points (-3, 5) and (-3, 8).
Example 8: Write the equation of the line through points (-3, 5) and (2,5).
Guided Practice
1) Write the equation of the line below.
6
2) Write the equation of the line below.
6
y
5
5
4
4
3
3
2
2
1
y
1
x
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
x
−6
−5
−4
−3
−2
−1
1
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
3) Write the equation of the line through
points (8, -2) and (8, 4).
2
3
4
5
6
4) Write the equation of the line
that is represented in the table.
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