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Re-write the first equation in slope-intercept format (y=mx+b):
3x + 5y =15
y = -3/5x -15/5
y = -3/5x + 3
The slope (m) = (-3/5)
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Since parallel lines have the same slope, the slope of the second line will also equal (-3/5).
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Use the slope-intercept formula to find the equation of the second line:
y = mx + b [Plug-in the values (0, 9) and the slope (-3/5).
9 = (-3/5)(0) + b [Solve for b]
9 = b.
So, the equation of the second line is:
y = (-3/5)x + 9

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Given point (0, 4) with a slope(m) of 8
(y2-y1) = m(x2-x1 [Use the point-slope format]
(y2-4) = 8(x2-0) [Plug-in the values]
y2 - 4= 8x - 0 [Simplify]
y-4 = 8x [Solve for y]
y = 8x+4 [Slope-intercept formula for the equation of a line]

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To find the y-intercept, first, rewrite in the slope-intercept format:
y=mx+b [Slope-intercept format where:
y = any y value of the line
m = the slope of the line
x = the corresponding x value of the line
b = the y-intercept of the line
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x – y = 4 [Isolate the "y" in order to re-write in the slope-intercept form]
-y=-x+4
-y/-1 = -x/-1 + 4/-1 [Simplify]
y = x - 4
Slope (m) = 1
y-intercpet = -4

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y = mx + b [Slope-intercept format]
y = any y value of the line
m = the slope of the line
x = any corresponding x value of the line
b = the y-intercpet (where the line crosses the y-axis
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y = mx + b
y = –5x + 9
-5 = the slope (m)
9 = the y-intecept (b)

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Given point (3, 0) and y-intercept (0, 2)
Since you are given two points, first find the slope:
m =(y2-y1)/(x2-x1)[Slope formula]
m = (2-0)/(0-3) [Plug-in the values]
m = 2/-3 or -2/3
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Next, use the slope-intercept format:
y = mx + b
0 = (-2/3)(3) + b [Plug-in the values using one of the points and the slope]
0 = -2 + b [Simplify]
2 = b [Solve for "b"]
y = (-2/3)x + 2 [Plug-in the values of "m" and the y-intercept for the equation of the line]

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Make sure each line is in the slope-intercept formate: y=mx+b. The "m" represents the slope value. If not, re-write it. The lines with the same slopes will be parallel.
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y = 4x – 8: m = 4
y = –4x + 8: m = -4
y = 4x + 5: m = 4
y = x – 8: m = 1
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So, y = 4x-8 and y = 4x+5 are parallel because they have the same slope.

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Given point (0, –7) with a slope of -7/2
(y-y)=m(x-x] [Use the point-slope formula]
(y-(-7)=(-7/2)(x-0) [Plug-in the points]
y+7 = -7/2x - 0 [Simplify]
y+7 = -7/2x
y = -7/2x - 7 [Solve for y][Final answer]

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1.(7x-2y+5)+(2x+5y-4) [Combine like-terms only]
9x+3y+1
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2.(3x+5xy+2y)+(4-3xy-2x) [Combine like-terms only]
x+2xy+2y+4
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3. -2[2a-(4a-2)-2(7-3a)] [Use the order of operations (PEMDAS)]
-2[2a-4a+2)-2(7-3a)][Multiply within the brackets]
-2[2a - 4a + 2 - 14 + 6a] [Combine like-terms]
-2[-2a - 12 + 6a)] [Combine like-terms]
-2[4a - 12] [Multiply outside of the brackets]
-8a + 24

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Sum = addition
"a number" = unknown number = x
So, 3+x

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[Change to an improper fraction]
[Cross-multiply]
[Multiply the denominators]
[Simplify]

[Combine fractions with the same denominator]
[Simplify] [Final answer]

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[Set the equation equal to zero by subtracting 16 from both sides]
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[Add the term (0x) to make it easier to work with]
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a=7
b=0
c=-25
[Plug-in the values]

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[Simplify]
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x = +26.4575/14 = 1.8898
x = -26.4747/14 = -1.8898

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Use this basic formula:
(% or rate of A)(Amount of A)+ (% or rate of B)(Amount of B) = C
C can equal (% or rate of C)(A+B) or C can equal (% or rate of C)(Amount of C)
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Change percentages to decimals: Example: 10% = .10
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Water is 0% acid.
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(0%)(xml) + (25%)(50ml) = (10%)(xml + 50ml)
(0)(x) + (.25)(50) = (.10)(x + 50)
0 + 12.50 = .10x + 5.0
12.50 = .10x + 5.0 [Solve for "x"]
7.5 = .10x
75ml = x
So, add 75ml of water (0% acid) to 50ml of a 25% acid to yield 125ml of a 10% acid.
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Check by plugging in all of the variables back into the original equation:
(%A)(Amount A) + (%B)(Amount B) = (%C)(A+B)
(0%)(75) + (.25)(50) = (.10)(125)
12.5 = 12.5 [Checks out]

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Factor
{Use the quadratic formula]
..
[Plug-in the values]
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[Simplify]
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[Reduce]
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x = 7/5

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Method #1:
Slope:-2;y-intercept:(0,4)
(y-y) = m(x-x) [Use the point-slope formula for the equation of the line]
(y-4) = (-2)(x-0) [Plug-in the values]
y-4 = -2x [Simplify]
y = -2x + 4 [Solve for "y"] [Final answer in slope-intercept form]
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Method #2:
Slope:-2;y-intercept:(0,4)
y=mx+b [Use the slope-intercept formula for the equation of the line]
y = -2x + 4 [Plug-in the values for the slope and the y-intercept]
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Solve for x:
2x – 3 = -4 [solve for x]
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2x – 3 + 3 = -4 + 3
2x = -1
2x/2 = -1/2
x = -1/2
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Check by pluggin-in (x=-1/2) back into the original equation.

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b-7 when b = 24
(24)-7 = 17 [Plug-in the value of "b"]

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y>-3x+4 [Re-write as an equality]
y=-3x+4
y=-3(0)+4 [Let (x=0) and solve for "y"]
y = 4
Plot the point (0, 4)
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y=-3x+4
0=-3x+4 [Let (y=0) and solve for "x"]
x = 4/3
Plot the point ((4/3), 0)
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Draw a dashed line for the line.
Since "y" is greater than (-3x+4), color or shade everything above and to the right of the dashed line.
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The diagram below only shows the boundary line. Your line should be a dashed line with shading above the line.
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(5,3) and (7,-8) [Points on a line]
m = (y2-y1)/x2-x1) [Formula for the slope of a line]
m = ((-8)-3)/(7-5) [Plug-in the values]
m = -11/2 [The slope of the line]
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y = mx+b [The slope-intercept formula for the equation of a line]
y = the y-value of a point on the line
m = the slope of the line
x = the corresponding x-value for a point on the line
b = the y-intercept; it is where the line crosses the y-axis (0, b)
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y = mx + b
3 = (-11/2)(5) + b [Pick a point and plug-in the values]
3 = (-55/2) + b [Solve for "b"]
(55/2) + (3) = b
61/2 = b
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y=(-11/2)x + (61/2) [Plug-in the values of the slope and y-intercept][Final answer]
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Check by plugging the values for either of the original points

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2x^2+7x-2=0
[The quadratic formula]
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Values:
a=2
b=7
c=-2
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[Plug-in the values]
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[Simplify]
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Two answers:

x = 0.2656
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or
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x=-3.766
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Check each value of x by plugging (x=0.2656) or (x=-3.766) back into the original equation.

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= =2
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Looking closer at the exponent of (1/2), the numerator represents the power or degree; the denominator represents the radical. So, "1" is the power, and "2" is the square root.

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Another example is:
= = 3

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a+4/2 = a+4/a [Find the lowest common denominator (LCD)]
(2*a) = LCD
(2a)(a+4)/2 = (2a)(a+4)/a [Multiply each fraction by the LCD]
(a)(a+4) = (2)(a+4) [Cancel wherever necessary]
a^2 + 4a = 2a + 8 [Simplify]
a^2 + 4a - 2a - 8 = 0 [Isolate all of the terms on one side of the equation]
a^2 + 2a - 8 = 0 [Combine like-terms]
(a-2)(a+4) = 0 [Factor]
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[Set each factor equal to zero and solve for "a"]
a-2=0
a=2
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or
a+4=0
a=-4
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So, a=2 or a=-4
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Check by plugging (a=2) or (a=-4) back into the original equation.
a=2
(2)+4/2 = (2)+4/(2)
6/2 = 6/2
3 = 3 [Checks out]
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a= -4
(-4)+4/2 = (-4)+4/(-4)
0/2 = 0/-4
0=0 [Checks out]

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3x - 7 = 2x + 8 [Move all of the variables to one side of the equation]
3x - 7 + 7 = 2x + 8 + 7 [Add 7 to both sides]
3x = 2x + 15
3x - 2x = 2x - 2x + 15
x = 15
Check by plugging in (x-15) back into the equation.
3(15) - 7 = 2(15) + 8
38 = 38 [Checks out]

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y+8=0 [Solve for y]
y+8-8=0-8 [Isolater the "y" by subtracting 8 from both sides]
y = -8
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Check by plugging (y=-8) back into the original equation.
(-8)+8 = 0
0=0 [Checks out]

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Follow the rules for multiplying integers:
Negative x Negative = Positive
Positive x Positive = Positve
Negative x Positive = Negative
Postive x Negative = Negative
The same rules also apply for dividing integers.
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(-5)(-3)(+2)
(15)(+2)
30

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Find the point of interception. That is, at which point do the lines cross?

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Yes, the algebraic method is more precise. When you "solve" a system you are really identifying the points that all of the lines have in common. In other words, the point at which the lines intersect.
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Finding the solution with graphs is not precise, but should usually be close enough if that is what is asked.

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2x + 4y = 2
Let x=0 and solve for y
Let y=0 and solve for x
Plot the two points:(0, 1/2) and (1,0)
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x + 2y = 1
Let x=0 and solve for y
Let y=0 and solve for x
Plot the two points:(0, 1/2) and (1, 0)

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1/8 - 3/5 = 1/x [Find the Least Common Denominator (LCD)]
1/8 - 3/5 = 1/x} [LCD = 8*5*x = 40x]
(40x)(1/8) - (40x)(3/5) = (40x)(1/x) [Multiply each term by the LCD]
5x - (8x)(3) = (40) [Cancel out wherever possible]
5x-24x=40 [Simplify]
-19x=40
x=-40/19
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Check by plugging (x=-40/19) back into the original equation and solve]
1/8 - 3/5 = 1/(-40/19)
-.475 = -.475

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m = (y2-y1)/x2-x1) [Use the slope of a line formula]
m = (-2-3)/(9-7) [Plug-in the values]
m = -5/2 = the slope
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y=mx+b [Use the slope-intercept formula to find the equation of the line]
3=(-5/2)(7) + b [Plug-in the values]
3=(-5/2) + b [Solve for b]
41/2 = b
y=mx+b [Plug-in the values for the slope and y-intercept (b) only]
y=(-5/2)x + 41/2 [Equation of the line]

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x>2 [Re-write the inequality as an equation]
x=2 [Graph using a dashed line. Shade everything above the line]
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2x + 3y > 6 [Solve for y]
y > -2/3x + 2 [Re-write the inequality as an equation]
y = -2/3x + 2 [Graph using a dashed line. Shade everything above the line]
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The reason you shade above the line is because the final inequalities are "greater than". If the inequality was "less than", than you would shade below the line.

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f(x) = x^2 + 4
Let:
a=1
b=0
c=4
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[Plug-in the values]
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[Simplify]
[Cancel out]
x = +-2i [x = -2i or x = +2i] [Final answers]
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g(x) = x^2 + x + 12
Let:
a = 1
b = 1
c = 12
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