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What is the parallel line for y = -4x + 1?

Parallel lines have equal slopes, therefore
a line parallel to y = -4x + 1, would have the same slope.

Slope-intercept form is y = mx + b
m is the slope
b is the y-interecept

In y = -4x + 1
slope = -4x

A line parallel to that, could be:
y = -4x
y = -4x + 7
y = -4x - 5
Any of those would be parallel to it.
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Is it possible to factor? If so how?

(8x - 5)(4x + 12)
= (8x - 5)(4)(x + 3) {factored 4 out of the second set of parentheses}
= 4(x + 3)(8x - 5) {re-arranged}
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solve the following equation for m


p = 6n - 5m/14
p - 6n = -5m/14 {subtracted 6n from both sides}
14p - 84n = -5m {multiplied both sides by 14}

14p - 84n
--------- = m {divided both sides by -5}
-5
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Solve the following equation for s


r = 10t - 3s/16
r - 10t = -3s/16 {subtracted 10t from both sides}
16(r - 10t) = -3s {multiplied both sides by 16}
16r - 160t = -3s {used distributive property}

16r - 160t
----------- = s {divided both sides by -3}
-3
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"A rectangle's length is 4 more than 4 times the width. The perimeter is 88 feet. What is the length and width of the rectangle? Use variables to label the rectangle. then show your work for checking your answer."

x = width
4x + 4 = length {length is 4 more than 4 times width}

Perimeter of a rectangle = 2(width) + 2(length)

2x + 2(4x + 4) = 88 {perimeter is 2(width) + 2(length)}
2x + 8x + 8 = 88 {used distributive property}
10x + 8 = 88 {combined like terms}
10x = 80 {subtracted 8 from both sides}
x = 8 {divided both sides by 10}
4x + 4 = 36 {substituted 8, in for x, into 4x + 4}

width = 8
length = 36

Perimeter of a rectangle
= 2(width) + 2(length)
= 2(8) + 2(36)
= 16 + 72
= 88
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multiply
-3x^2(2x + 2)
= -3x^2(2x) - 3x^2(2) {used distributive property}
= -6x^3 - 6x^2 {multiplied and added the exponents when multiplying}
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Like terms have the same variable and exponent.

7x^3 +3x^3 + 3
= 10x^3 + 3 {combined 7x^3 and 10x^3}
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x^2 + 13x + 30 = 0
(x + 10)(x + 3) = 0 {factored into two binomials}
x + 10 = 0 or x + 3 = 0 {set each factor equal to 0}
x = -10 or x = -3 {solved each equation for x}
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"FIND THE SLOPE OF Y=-5"

Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

y = -5
y = 0x - 5 {put a 0x in, to show the slope}
m = 0

slope = 0
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"graph line passing through given point and having given slope (0,1), m=4"

(0,1) , m = 4

To graph:
- put a point on (0,1)
- from there, go up 4 and to the right one, and put another point,
since the slope is 4 {that is 4/1 as rise/run}
- draw a line through the two points
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graph by using slope and y-intercept.
2x + y = -5

Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

2x + y = -5
y = -2x - 5 {got in slope-intercept form}
slope = -2 or -2/1 {rise over run}
y-intercept = -5

To graph:
- put a point on -5 on the y-axis, that is the y-intercept
- from there, go down 2 and to the right 1 and put another point,
since the slope is -2/1
- draw a line through the two points
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62% of 294
= 294(.62) {changed 62% to decimal by moving decimal point left two, and multiplied by 294}
= $182.28 {multiplied}
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Solve the equation.
9x = 3x^3
3x^3 - 9x = 0 {subtracted 9x from both sides}
3x(x^2 - 9) = 0 {factored 3x out}
3x(x + 3)(x - 3) = 0 {factored x2 - 9 into two binomials}
3x = 0 or x + 3 = 0 or x - 3 = 0 {set each factor equal to 0}
x = 0 or x = -3 or x = 3 {solved each equation for x}
x = 0,-3, or 3
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20x - 3(7x + 6) < -8x + 16
20x - 21x - 18 < -8x + 16 {used distributive property}
-x - 18 < -8x + 16 {combined like terms}
-x < -8x + 34 {added 18 to both sides}
7x < 34 {added 8x to both sides}
x < 34/7 {divided both sides by 7}
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3 3/4 divided by 1 5/7

3 3/4 ÷ 1 5/7
= 15/4 ÷ 12/7 {changed to improper fractions}
= 15/4 x 7/12 {multiplied by reciprocal}
= 35/16 {cancelled 15 and 12 and multiplied what's left}
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"the equation of the horizontal line passing through the point (-1,-8)"

y = -8 is the equation of the horizontal line passing through the point (-1,-8)

A horizontal line will start off "y = " and then be the y-coordinate
on the other side of the equal sign

A vertical line will start off "x = " and then be the x-coordinate
on the other side of the equal sign.
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"The equation of the vertical line passing through the point (3,1)"

x = 3 is the equation of the vertical line through the point (3,1)

A vertical line will start off "x = " and then be the x-coordinate
on the other side of the equal sign.

A horizontal line will start off "y = " and then be the y-coordinate
on the other side of the equal sign
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To get the x-intercept, put 0 in for y
To get the y-intercept, put 0 in for x

2y + 3x = -2

For the x-intercept:
2(0) + 3x = -2 {substituted 0 in for y}
3x = -2 {multiplied 2 by 0}
x = -2/3 {divided both sides by 3}
x-intercept is (-2/3,0)

For the y-intercept:
2y + 3(0) = -2 {substituted 0 in for x}
2y = -2 {multiplied 3 by 0}
y = -1 {divided both sides by 2}
y-intercept is (0,-1)
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This is one way to do it:
(1,2), m = 1/3

y - y1 = m(x - x1) is point-slope form

y - 2 = 1/3(x - 1) {substituted point and slope into point-slope form}
y - 2 = 1/3x - 1/3 {used distributive property}
y = 1/3x + 5/3 {added 2 to both sides}
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Use a proportion:

60 lbs / 100 gal = x lbs / 1 gal
100x = 60 {cross-multiplied}
x = .6 {divided both sides by 100}

.6 lbs is to be used

or

16 oz = 1 lb.
.6(16) = 9.6 ounces is to be used
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"the second of two numbers is two more than three times the first number. Their sum is negative twenty-two"

x = first number
3x + 2 = second number {2nd is two more than three times first}

x + 3x + 2 = -22 {sum is negative twenty-two}
4x + 2 = -22 {combined like terms}
4x = -24 {subtracted 2 from both sides}
x = -6 {divided both sides by 4}
3x + 2 = -16 {substituted -6, in for x, into 3x + 2}

-6 and -16 are the two numbers
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"five more than three times a number n is thirty"

n = the number

3n + 5 = 30 {five more than three times a number "n" is thirty}
3n = 25 {subtracted 5 from both sides}
n = 25/3 {divided both sides by 3}

the number is 25/3
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"A 13-foot board is cut into two pieces. If one piece is x feet long, express the other length in terms of x. "

x = one piece
13 - x = other piece {the original 13 foot piece minus the other cut piece}
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"John is 5 times as old as he was 40 years ago so how old is he now"

x = his age now
x - 40 = his age 40 years ago

x = 5(x - 40){now, he is five times his age 40 years ago}
x = 5x - 200 {used distributive property}
-4x = -200 {subtracted 5x from both sides}
x = 50 {divided both sides by -4}

John is 50 now
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D is not a linear equation,
because of the x^2
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"the sum of two numbers is 25. The greater number is 10 less than the product of 6 and the smaller number. Find the smaller number"

x = one number
6x - 10 {greater number is 10 less than product of 6 and smaller}

x + 6x - 10 = 25 {sum of two numbers is 25}
7x - 10 = 25 {combined like terms}
7x = 35 {added 10 to both sides}
x = 5 {divided both sides by 7}

the smaller number is 5
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15 > -m + 6
9 > -m {subtracted 6 from both sides}
-9 < m {divided both sides by -1 and changed the inequality sign}
m > -9 {flipped entire inequality around, so that m is first}

Note
- Whenever you multiply or divide both sides of an inequality by a
negative number, you have to change the inequality sign
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"The sum of two numbers is 32 and the difference is 14. Find the two numbers...... Thank You very much"

x = one number
y = other number

x + y = 32 {sum of two numbers is 32
x - y = 14 {difference is 14}
-----------
2x = 46 {added the two equations together}
x = 23 {divided both sides by 2}

x + y = 32 {top equation}
23 + y = 32 {substituted 23, in for x, into top equation}
y = 9 {subtracted 23 from both sides}

23 and 9 are the two numbers
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"Marge is twice as old as consuelo.the sum of their ages seven years ago was 13 how old are they now ?

x = Consuelo's age now
2x = Marge's age now

x - 7 = Consuelo's age 7 yrs ago
2x - 7 = Marge's age 7 yrs ago

x - 7 + 2x - 7 = 13 {sum of ages 7 yrs ago was 13}
3x - 14 = 13 {combined like terms}
3x = 27 {added 14 to both sides}
x = 9 {divided both sides by 3}
2x = 18 {substituted 9, in for x, into 2x}

Consuelo is 9 now
Marge is 18 now
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"Find a number such that twice its square root is 28."


x = the number

2√x = 28 {twice the number's square root is 28}
√x = 14 {divided both sides by 2}
x = 196 {squared both sides}

196 is the number
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"Andy is four times as old as Wendy . In twelve years Wendy's age will be half of Andy's.find their ages now."

x = Wendy's age now
4x = Andy's age now

x + 12 = Wendy's age in 12 years
4x + 12 = Andy's age in 12 years

x + 12 = (1/2)(4x + 12) {in twelve years, Wendy's age will equal half Andy's age}
x + 12 = 2x + 6 {used distributive property}
12 = x + 6 {subtracted x from both sides}
x = 6 {subtracted 6 from both sides}
4x = 24 {substituted 6, in for x, into 4x}

Wendy is 6 now and Andy is 24 now
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