Transcript Alg2-Ch.2-Sect.4-Power_Point_Lesson

2-4
2-4 Writing
Writing Linear
Linear Functions
Functions
Warm Up
Lesson Presentation
Lesson Quiz
Worksheet
Holt
Algebra
Holt
Algebra
2 2
2-4
Writing Linear Functions
*Warm Up
Write each function in slope-intercept form.
1. 4x + y = 8
2. –y = 3x
3. 2y = 10 – 6x
Determine whether each line is vertical or
horizontal.
3
4. x =
4
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5. y = 0
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Writing Linear Functions
Objectives
Use slope-intercept form
y = mx + b
and point-slope form
y–y1 = m(x–x1)
to write linear functions.
Write linear functions to solve problems.
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Writing Linear Functions
Example 1: Writing the Slope-Intercept Form of the
Equation of a Line
Write the equation of the graphed line in slopeintercept form.
Step 1 Identify the y-intercept.
(The point where the line
crosses the y-axis.)
1
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Example 1 Continued
Step 2
Find the slope.
Choose any two convenient
points on the line, such as
(0, 1) and (4, –2). Count from
(0, 1) to (4, –2) to find the
rise and the run. The rise is –3
units and the run is 4 units.
3
4
–4
–3
Slope is rise = –3 = – 3 .
run
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Example 1 Continued
Step 3
Write the equation in slope-intercept form.
y = mx + b
3
y=– x+1
4
m= –
3
and b = 1.
4
The equation of the line is y = –
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3
x + 1.
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Check It Out!
Write the equation of the graphed line in slopeintercept form.
Step 1 Identify the y-intercept.
Step 2 Find the slope.
Step 3
Write the equation in
slope-intercept form.
y = mx + b
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Writing Linear Functions
Rise is the differences in the y-coordinates
Run is the differences in the x-coordinates.
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Helpful Hint
If you reverse the order of the points, the slope
is still the same.
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Find the slope of the line through
(–1, 1) and (2, –5).
The slope of the line is –2.
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Example 2B: Finding the Slope of a Line Given Two or
More Points
Find the slope of the line.
x
4
8
12
16
y
2
5
8
11
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Choose any
two points.
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Example 2C: Finding the Slope of a Line Given Two or
More Points
Find the slope of the line shown.
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Check It Out! Example 2A
Find the slope of the line.
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x
y
–6
–3
–4
–1
–2
1
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Check It Out! Example 2B
Find the slope of the line through (2,–5) and
(–3, –5).
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Because the slope of line is constant, it is
possible to use any point on a line and the
slope of the line to write an equation of the
line in point-slope form.
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Holt Algebra 2
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Writing Linear Functions
Example 3: Writing Equations of Lines
Write the equation of the line that contains
the points in the table.
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x
–8
–4
y
–5
–3.5
4
–0.5
8
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Writing Linear Functions
x
–8
–4
y
–5
–3.5
Method A Point-Slope Form
Using (8, 1):
4
–0.5
8
1
Rewrite in slopeintercept form.
y – y1 = m(x – x1)
Distribute.
Substitute.
Simplify.
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Solve for y.
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Writing Linear Functions
x
–8
–4
y
–5
–3.5
4
8
–0.5
1
Method B Slope-intercept Form
Using (8, 1), solve for b.
y = mx + b
Rewrite the equation
using m and b.
y = mx + b
Substitute.
1=3+b
Simplify.
b = –2
Solve for b.
The equation of the line is
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Check It Out! Example 3a
Write the equation of the line in slope-intercept
form with slope –5 through (1, 3).
Holt Algebra 2
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Check It Out! Example 3b
Write the equation of the line in slope-intercept
form through (–2, –3) and (2, 5).
Holt Algebra 2
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Example 4A: Entertainment Application
The table shows the rents and selling prices
of properties from a game.
Selling Price
Rent
($)
($)
Express the rent as a function
75
9
of the selling price.
Let x = selling price and y = rent.
Find the slope by choosing two
points. Let (x1, y1) be (75, 9)
and (x2, y2) be (90, 12).
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90
12
160
26
250
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Example 4A Continued
To find the equation for the rent function, use
point-slope form.
y – y1 = m(x – x1)
Use the data in the first
row of the table.
Simplify.
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Example 4B: Entertainment Application
Graph the relationship between the selling
price and the rent. How much is the rent for a
property with a selling price of $230?
To find the rent for a property, use the graph or
substitute its selling price of $230 into the function.
Substitute.
y = 46 – 6
y = 40
The rent for the property is $40.
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Check It Out! Example 4a
Express the cost as a linear
function of the number of
items.
First, calculate the slope.
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Items
Cost ($)
4
14.00
7
21.50
18
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Check It Out! Example 4a Continued
Find the equation for the number of items:
Method #1
y – y1 = m(x – x1)
Method #2
y = mx + b
y – 14 = 2.5(x – 4)
14 = 2.5(4) + b
y – 14 = 2.5(x) – 2.5(4)
14 = 10 + b
y – 14 = 2.5(x) – 10
-10 = -10
+ 14 =
+ 14
y = 2.5x + 4
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4=b
y = 2.5x + 4
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Check It Out! Example 4b
Graph the relationship between the number of
items and the cost. Find the cost of 18 items.
To find the cost, use the graph or substitute
the number of items into the function.
y = 2.5(18) + 4
Substitute.
y = 45 + 4
y = 49
The cost for 18 items is $49.
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By comparing slopes, you can determine if the
lines are parallel or perpendicular. You can also
write equations of lines that meet certain
criteria.
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Holt Algebra 2
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Example 5A: Writing Equations of Parallel and
Perpendicular Lines
Write the equation of the line that’s parallel to
y = 1.8x + 3 and that passes through (5, 2)
m = 1.8
Parallel lines have equal slopes.
Use y – y1 = m(x – x1) with (x1, y1) =
y – 2 = 1.8(x – 5)
(5, 2).
y – 2 = 1.8x – 9
y = 1.8x – 7
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Distributive property.
Simplify.
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Example 5B: Writing Equations of Parallel and
Perpendicular Lines
Write the equation of the line that’s perpendicular
to
and passing through (9, –2)
The slope of the given line is
, so the slope of
the perpendicular line is the opposite reciprocal,
Use y – y1 = m(x – x1). y + 2 is
equivalent to y – (–2).
Distributive property.
Simplify.
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Check It Out! Example 5a
Write the equation of the line parallel to y = 5x – 3
and passing through (1, 4)
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Example 5B: Writing Equations of Parallel and
Perpendicular Lines
Write the equation of the line that’s perpendicular
to
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and through (9, –2)
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Check It Out! Example 5b
Write the equation of the line that’s perpendicular
to
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and passing through (0, –2)
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Lesson Quiz: Part I
Write the equation of each line in slopeintercept form.
1.
2. parallel to y = 0.5x + 2 and through (6, 1)
3. perpendicular to
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and through (4, 4)
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Lesson Quiz: Part II
4. Express the catering cost as a function of
the number of people. Find the cost of
catering a meal for 24 people.
Number in Group
Cost ($)
4
7
15
98
134
230
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Worksheet
2.4B
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Holt Algebra 2