4-3A Writing Equations in Slope-Intercept Form

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4-3A Writing Equations in Slope-Intercept Form
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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In the previous lesson you wrote direct variation
equations.
In todays lesson, when you know the slope and
the y-intercept you will be able to write the
equation of a line.
Do you remember y-intercept?
y










The y-intercept is the y-coordinate of the point
where the line crosses the y-axis.

x
3
The linear equation ymxb is written in
slope-intercept form where m is the slope and b
is the y-intercept.
y-intercept
slope
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slope
y-intercept
If y x 3 then
the slope is
and
the y-intercept is
Slope is a numerical value do not include the
variable x.
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slope
y-intercept
If y 2x 3 then

and the y-intercept is
the slope is
The slope is a numerical value do not include
the variable x.
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How to write the equation of a line given the
slope and the y-intercept.
Write the slope-intercept form.
Substitute the slope for m and the y-intercept
for b.
Simplify undo the double sign.
Write the equation of the line whose slope is 9
and whose y-intercept is 6 .
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Write an equation in slope-intercept form of the
line with the given slope and y-intercept.
Example 2 slope
Example 1 slope 7 , y-intercept 2
, y-intercept 10
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An online store charges 3 per order plus 1.00
per book for shipping. Write a linear equation
in slope-intercept to model the situation.
y
Constant rate of change is slope.
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Let x represent number of books and y represent
cost of shipping.










9
8
7
Shipping costs (dollars)
6
5
Find the y-intercept.
4

3
The charge per book is the slope, so m 1.
2
1
x
6
8
10
2
4
0
of books
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Example 3 You want to rent a rowboat for a
fishing trip. There is an initial fee of 25,
plus a 50 daily fee. Write a linear equation
for this situation where y represents the cost of
renting a rowboat and x represents the number of
days rented.
Example 4 Jenny opened a savings account with
200 and plans on saving 100 per month. Write a
linear equation for this situation where y
represents the savings and x represents the
number of months.
Constant rate of change is slope.
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Example 3 You want to rent a rowboat for a
fishing trip. There is an initial fee of 25,
plus a 50 daily fee. Write a linear equation
for this situation where y represents the cost of
renting a rowboat and x represents the number of
days rented.
y
Constant rate of change is slope.
Find the y-intercept.










225
200
175
150
Rental cost (dollars)
125
100
75
50

25
x
3
4
5
1
2
0
days
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Example 4 Jenny opened a savings account with
200 and plans on saving 100 per month. Write a
linear equation for this situation where y
represents the savings and x represents the
number of months.
y
Constant rate of change is slope.










900
Find the y-intercept.
700
savings (sollars)
500
300

(0,200)
100
x
3
4
1
2
5
0
time (months)
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Write 2x y -3 in slope-intercept form. The
identify the slope and y-intercept.
Write the equation.
Rewrite in slope-intercept form (solve for y).
1
Identify the slope and y-intercept.
You must write the variable term first.
y-intercept is 3
slope is 2
Copy the above in your spiral notebook!
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Write the equation in slope-intercept form. Then
identify the slope and y-intercept.
Example 5
Example 6
b 2
b 2
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When a graph clearly indicates the y-intercept
and another point on the line, you can use the
graph to write an equation of the line.
y
Recall that the y-intercept is the y-coordinate
of the point where the line crosses the y-axis.











x
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Write the equation of the line shown in the graph
using slope-intercept form.
y











Write the slope-intercept form.
Locate the y-intercept.
Locate another point on the graph.
x

Substitute the slope and y-intercept in the slope
intercept form.
Simplify - undo double sign. Use good form
place negative out front!
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Write the equation of the line shown in the graph
using slope-intercept form.
Example 8
Example 7
y
y






















x
x


y-intercept 3
y-intercept -2
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Notice that the scales on the axes are different.
In this case it would be difficult to calculate
slope by walking the line (counting squares).
Instead use the slope formula.
y










4
x
1
1
4
Scales on the axes different use slope formula!
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Example 9 Write the equation of the line shown
in the graph using slope-intercept form.
y
Write the slope-intercept form.











Locate the y-intercept.
8
(0,8)
4
Locate another point on the line.
1
x
1

Write the coordinates of both points.
4
(4,4)
(0,8)
(4,4)
Use the slope formula to calculate the slope.
Substitute the slope and y-intercept in the slope
intercept form.
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When the scales on the axes are different, you
must use the slope formula. Could you use the
slope formula if the scales are the same?
y










1
x
1
1
1
Yes, but it would be more work!
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Write the equation of the line in the graph.
y
What axis does the line intercept?










y
What is the y intercept?
Write the equation.
x

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Write the equation of the line in the graph.
Example 10
Example 11
y
y






















x
x
What axis does the line intercept?
What axis does the line intercept?
y
x
What is the y-intercept?
What is the x-intercept?
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Example 12 What special name is given to the
graph of x 0?











y-axis


x

y
Think of some coordinates. (0,1), (0,0), (0,1),
(0,2)
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Example 13 What special name is given to the
graph of y 0?
x-axis














x
y
Think of some coordinates. (1,0), (0,0), (1,0),
(2,0)
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Homework
4-A5 Pages 207208 12-23 and Handout A5.