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GED Math : Algebra

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Standard Form

Rewrite the equation in standard form: y=3x+8

Possible Answers:

-3x+y =8

-3x-y =8

3x+y =8

-3x+y =-8

$\textup{The equation is already in standard form.}$

Correct answer:

-3x+y =8

Explanation:

To rewrite in standard form, we will need the equation in the form of:

Ax+By =C

Subtract on both sides.

y-3x=3x+8-3x

Regroup the variables on the left, and simplify the right.

The answer is: -3x+y =8

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Example Question #6 : Standard Form

Rewrite the equation in standard form.

y-2=3(x+6)

Possible Answers:

3x+y = 16

-3x+y = 16

-3x+y = -20

-3x+y = 20

3x-y = 16

Correct answer:

-3x+y = 20

Explanation:

The given equation is in point-slope form.

The standard form is: Ax+By = C

Distribute the right side.

y-2=3x+18

Subtract on both sides.

y-2-3x=3x+18-3x

-3x+y-2 = 18

Add 2 on both sides.

-3x+y-2+2 = 18+2

The answer is: -3x+y = 20

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Example Question #7 : Standard Form

Rewrite the equation in standard form: 3+y-9x=4

Possible Answers:

9x-y = -1

9x-y = 7

9x-y = -7

-9x-y = 7

9x-7y = -1

Correct answer:

9x-y = -1

Explanation:

The standard form of a linear equation is: Ax+By =C

Reorganize the terms.

Add on both sides.

3+y-9x+(9x)=4+(9x)

3+y= 4+9x

Subtract on both sides.

3+y-y= 4+9x-y

3= 4+9x-y

Subtract four on both sides.

3-4= 4+9x-y-4

The answer is: 9x-y = -1

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Example Question #1 : Standard Form

Given the slope of a line is and a point is (4,-3) , write the equation in standard form.

Possible Answers:

-2x+y = -11

-2x+y = -22

2x-2y = -11

-2x+3y = -11

2x-y = -11

Correct answer:

-2x+y = -11

Explanation:

Write the slope-intercept form of a linear equation.

y=mx+b

Substitute the point and the slope.

-3 = (2)(4)+b

Solve for the y-intercept, and then write the equation of the line.

-3 = 8+b

-3-8 = 8+b-8

b=-11

y=2x-11

The equation in standard form is: Ax+By =C

Subtract from both sides.

y-2x=2x-11-2x

The answer is: -2x+y = -11

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Example Question #1 : Standard Form

Which of the following is NOT in standard form?

Possible Answers:

y=5x^2-3x+5

$\textup{All equations are represented in standard form.}$

-19x+y = 3

y-2=3(x+9)

15x-y=15

Correct answer:

y-2=3(x+9)

Explanation:

The equation in standard form of a linear equation is:

Ax+By =C

The equation in standard form of a parabolic equation is:

y= Ax^2+Bx+C

All of the following equations are in standard form except:

y-2=3(x+9)

This equation is in point-slope format: y-y_1 = m(x-x_1)

The answer is: y-2=3(x+9)

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Example Question #5 : Standard Form

Write the following equation in standard form.

y-2 = 3(x-3)

Possible Answers:

3x+2y =8

x-3y = -7

3x-y = -11

3x-y = -7

-3x+y = -7

Correct answer:

-3x+y = -7

Explanation:

The standard form of a linear equation is: Ax+By =C

Distribute the right side.

y-2 = 3x-9

Subtract on both sides.

y-2 -(3x)= 3x-9-(3x)

-3x+y-2 = -9

Add 2 on both sides.

-3x+y-2+2 = -9+2

The answer is: -3x+y = -7

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Example Question #51 : Linear Algebra

Determine the equation in standard form: 3x-6y = 14

Possible Answers:

$y=\frac{1}{2}x+\frac{7}{3}$

$y+\frac{14}{3} = \frac{1}{2}(x)$

$\textup{No changes are needed.}$

$y=\frac{1}{2}x-\frac{7}{3}$

$y-\frac{14}{3} = \frac{1}{2}(x)$

Correct answer:

$\textup{No changes are needed.}$

Explanation:

The equation in standard form is defined as Ax+By =C .

The given equation is already in standard form and does not require any change to the variables.

Do not put this equation in point-slope, or the slope-intercept form.

The answer is: $\textup{No changes are needed.}$

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Example Question #221 : Algebra

Write the equation in standard form: y=-2x-5

Possible Answers:

-2x+y = -5

2x-y = 5

2x-2y = 5

2x+y = -5

2x-y = -5

Correct answer:

2x+y = -5

Explanation:

The standard form of a line is defined as: Ax+By=C

Add on both sides.

y+2x=-2x-5+2x

Rearrange the terms.

The answer is: 2x+y = -5

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Example Question #11 : Standard Form

Rewrite the equation in standard form. $-3x =\frac{1}{4}y-2x$

Possible Answers:

20x+y=4

$\textup{The answer is not given.}$

$-5x-\frac{1}{4}y = 1$

4x+y=0

$-5x+\frac{1}{4}y = 1$

Correct answer:

4x+y=0

Explanation:

The equation in standard form is: Ax+By=C

Add on both sides.

$-3x+3x =\frac{1}{4}y-2x+3x$

Simplify both sides.

$0=\frac{1}{4}y+x$

If we multiply by four on both sides, we can eliminate the fraction.

$0\cdot 4=4(\frac{1}{4}y+x)$

0 = y+4x

The answer is: 4x+y=0

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Example Question #12 : Standard Form

What is the equation $y=\frac {1}{3}x+\frac {4}{5}$ in standard form?

Possible Answers:

-5x+15y=-12

5x-15y=12

-5x+15y=12

$-\frac {1}{3}x+y=\frac {4}{5}$

Correct answer:

-5x+15y=12

Explanation:

Step 1: Find the lowest common denominator of the fractions on the right. To find the lowest common denominator in this question, we multiply the denominators together because both denominators are both prime numbers. **In the cases where the denominators are either both composite or one prime/one composite, find the lowest common denominator by breaking down the factors of the two numbers and taking the product of the factors that are in common (sometimes you will need to add an uncommon factor).

So, lowest common denominator is $3\times5=15$ .

Step 2: Multiply both sides by 15.

$(15)y=(15)\times\frac {1}{3}x+(15)\times\frac {4}{5}$

Step 3: Simplify:

15y=5x+12

Step 4: Standard form is given when x and y are on the same side of the equation, usually written as Ax+By=C .

So, we need to move the over, and then we have our answer:

15y-5x=(5x-5x)+12

$\Rightarrow -5x+15y=12$

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All GED Math Resources

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GED Math : Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #5 : Standard Form

Example Question #6 : Standard Form

Example Question #7 : Standard Form

Example Question #1 : Standard Form

Example Question #1 : Standard Form

Example Question #5 : Standard Form

Example Question #51 : Linear Algebra

Example Question #221 : Algebra

Example Question #11 : Standard Form

Example Question #12 : Standard Form

All GED Math Resources

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