Download Slope-Intercept Form

Name ________________________________________ Date __________________ Class __________________
LESSON
6-1
Slope-Intercept Form
Practice and Problem Solving: C
Write the equation for each line in slope-intercept form. Then identify
the slope and the y-intercept.
y
x
1. 3(x − 2y) = 5(x − 3y) + 9
2.
−
=1
5
7
Equation: ____________________________
Equation: ____________________________
Slope: _______________________________
Slope: _______________________________
y-intercept: __________________________
y-intercept: __________________________
Write an equation for each line. Then graph the line.
3. A line whose slope and y-intercept
are equal and the sum of the two is −4
4. A line that has a slope half as great as
its y-intercept and the sum of the two is 1
________________________________________
________________________________________
Let f(x) = mx + b be a function with real numbers for m and b. Use this
for Problems 5 and 6.
5. Show that the domain of this function is the set of all real numbers.
_________________________________________________________________________________________
_________________________________________________________________________________________
6. Show that the range of the function may or may not be the set of all
real numbers.
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_________________________________________________________________________________________
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
97
6.
MODULE 5 Challenge
1 a. $30,000
b. $165,000
c. $1,515,000
2. The fixed costs are spread over a greater
number of units.
3 a. $54,500
b. $545,000
c. $5,450,000
4. 28 units
7. slope is 3, y-intercept is −5
5 a. no
b. yes
8. y = 0.25x − 11
c. yes
9. f ( x ) = 30,000 − 500 x
6. for 100 units, $24,500; for 1000 units,
$380,000
Practice and Problem Solving: C
MODULE 6 Forms of Linear
Equations
LESSON 6-1
1. y =
2
2
x + 1; slope: ; y-intercept: 1
9
9
2. y =
7
7
x − 7; slope: ; y-intercept: −7
5
5
3. y = −2x − 2
Practice and Problem Solving: A/B
1. y = −4x + 7; slope: −4; y-intercept: 7
2. y =
2
2
x − 3; slope: ; y-intercept: −3
3
3
3. y =
5
3
5
3
x − ; slope: ; y-intercept: −
4
2
4
2
4. y = −
1
1
x + 4; slope: − ; y-intercept: 4
2
2
5.
4. y =
1
2
x+
3
3
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
519
5. Suppose x is any real number. Since m is
also a real number, mx can be found.
And, since b is a real number, mx + b can
then be found. So, all real numbers are in
the domain of f.
14. slope: −
2
; y-intercept: 3
5
f (x) − b
. Then
m
suppose that f ( x ) is any real number.
You can subtract b from it to get f ( x ) − b,
and you can then divide f ( x ) − b by m to
f (x) − b
, as long as m ≠ 0.
get
m
6. Rewrite the function as x =
So, the range of the function is all real
numbers as long as m ≠ 0. If m = 0, then
the function becomes f ( x ) = b and its
range is the single real number b.
15. The graph is a line. Its slope would
increase from 2 to 2.5, making the line
steeper.
Reading Strategies
Practice and Problem Solving: Modified
1. y = −2x + 4
1. With a fraction, you have a “rise” and “run”
for graphing.
2. y = −8x + 17
2. (0, −8)
3. 5; 12
3. y = 3x − 11
4. −3; 0
1
6. ; 3
3
5. 1; −4
4. y = −
5
x +1
4
5. y =
1
x −3
2
6. y =
1
1
x−
4
10
7.
7. −10
8. −1
9. 4
10. −8
11. 2
8.
12. −14
13. slope: 3; y-intercept: −5
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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