Math Jewels

       Math Jewels
                                                                By: Julie
On this page, I will explain how to solve a Linear Equation, solve Literal Equations, and write an equation of a line.

Linear Equations

x+4= 9 write the problem

-4 -4 isolate the variable by subtracting four from both sides

   x = 5 the answer is x = the answer

6x-4 = 2x+10 problem

   +4       +4 isolate variable by adding 4 to both sides

6x = 2x+14 new problem

-2x   -2x isolate the number so that if is variable = number

4x = 14
4       4 rid the x of the number: divide by 4 on both sides

x = 3.5 answer

2(x+6) = -2(x-4) problem

2x+12 = -2x+8 distribute the 2 and -2 through the problem using distributive property

     -12         -12 isolate the variable: subtract 12

2x = -2x-4 new problem

+2x +2x isolate the number: add 2x

4x = -4
4     4 isolate the variable: divide by 4

x = -1 answer

Literal Equations

4x+8y = 17; solve for y problem

-4x         -4x isolate the variable that is to be solved by subtracting 4x

8y = -4x+17
8      8   8 isolate the variable that is to be solved by dividing by 8

y = -1/2 x + 17/8 answer

E = IR ; solve for I
R    R - Problem
- isolate the variable to be solved: divide by R

I = E
     R answer

F = G Mp x R    ; solve for G
x R         R - problem
- rid the problem of the denominator of the fraction: multiple both sides by R

FR = G Mp
Mp     Mp isolate the variable by dividing by Mp

G = FR
      Mp answer

The Equation of the Line
Slope-intercept form: y = mx+b
        - m = the slope
        - b = y-intercept
Point-slope form: y-y₁= m(x-x₁)
         - m = slope
        - (x₁-y₁) is the point on the line
Standard form: ax+by = c
         - a, b, c = numbers
         - ax = the slope
         - by = the answer of slope intercept after distribution
         - c = the y-intercept
- All forms will be found for each problem.

point: (-6, 5), m=3 problem

y-5 = 3(x+6) substitute points and slope into point-slope form

y-5 = 3x+18
+5       +5 - distribute using distributive property
- isolate y by adding 5

y = 3x+23 slope intercept form

-3x    -3x to get to standard from: x andy have to be on the same side - so, subtract 3x from both sides

-3x+y = 23 there can be no negative or fractions in the front of standard form:so, multiply all numbers by -1

3x-y = -23 standard form

find the equation of the line that passes through (8,5),(11,14) problem

14-5 = 9 = 3
11-8    3 find the slope by substituting into the slope formula: y₁-y₂
                           x₁-x₂

y-5 = 3(x-8) substitute into point-slope form

y-5 = 3x-24
+5    +5 - distribute
- isolate the y

y = 3x-19 slope-intercept form

-3x   -3x put the x and y together form standard form

-3x+y = -19 no negatives or fractions in front: multiply by -1

3x-y = 19 standard form

find the equation of the line for (1,-1) and is perpendicular to line    y = -(1/2)x+6 -problem
- to find the slope of the perpendicular line, flip the slope and multiply by -1

y+1 = 2(x-1) point-slope form

y+1 = 2x-2
-1    -1 - distribute
- isolate the y

y = 2x-3 slope-intercept form

-2x -2x put the x and y on the same side

-2x+y = -3 no negative of fraction in front

2x-y = 3 standard form

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E = IR ; solve for I R R	- Problem - isolate the variable to be solved: divide by R
I = E R	answer

F = G Mp x R ; solve for G x R R	- problem - rid the problem of the denominator of the fraction: multiple both sides by R
FR = G Mp Mp Mp	isolate the variable by dividing by Mp
G = FR Mp	answer

x+4= 9	write the problem
-4 -4	isolate the variable by subtracting four from both sides
x = 5	the answer is x = the answer

6x-4 = 2x+10	problem
+4 +4	isolate variable by adding 4 to both sides
6x = 2x+14	new problem
-2x -2x	isolate the number so that if is variable = number
4x = 14 4 4	rid the x of the number: divide by 4 on both sides
x = 3.5	answer

2(x+6) = -2(x-4)	problem
2x+12 = -2x+8	distribute the 2 and -2 through the problem using distributive property
-12 -12	isolate the variable: subtract 12
2x = -2x-4	new problem
+2x +2x	isolate the number: add 2x
4x = -4 4 4	isolate the variable: divide by 4
x = -1	answer

4x+8y = 17; solve for y	problem
-4x -4x	isolate the variable that is to be solved by subtracting 4x
8y = -4x+17 8 8 8	isolate the variable that is to be solved by dividing by 8
y = -1/2 x + 17/8	answer

point: (-6, 5), m=3	problem
y-5 = 3(x+6)	substitute points and slope into point-slope form
y-5 = 3x+18 +5 +5	- distribute using distributive property - isolate y by adding 5
y = 3x+23	slope intercept form
-3x -3x	to get to standard from: x andy have to be on the same side - so, subtract 3x from both sides
-3x+y = 23	there can be no negative or fractions in the front of standard form:so, multiply all numbers by -1
3x-y = -23	standard form

find the equation of the line that passes through (8,5),(11,14)	problem
14-5 = 9 = 3 11-8 3	find the slope by substituting into the slope formula: y₁-y₂ x₁-x₂
y-5 = 3(x-8)	substitute into point-slope form
y-5 = 3x-24 +5 +5	- distribute - isolate the y
y = 3x-19	slope-intercept form
-3x -3x	put the x and y together form standard form
-3x+y = -19	no negatives or fractions in front: multiply by -1
3x-y = 19	standard form

find the equation of the line for (1,-1) and is perpendicular to line y = -(1/2)x+6	-problem - to find the slope of the perpendicular line, flip the slope and multiply by -1
y+1 = 2(x-1)	point-slope form
y+1 = 2x-2 -1 -1	- distribute - isolate the y
y = 2x-3	slope-intercept form
-2x -2x	put the x and y on the same side
-2x+y = -3	no negative of fraction in front
2x-y = 3	standard form