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GED Math : Standard Form

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1 : Standard Form

Which of the following is an example of an equation of a line written in standard form?

Possible Answers:

$\small y=\frac{1}2x+\frac{7}{4}$

$\small x=-2y+\frac{7}{2}$

$\small 2x+4y-7=0$

$\small 2x+4y=7$

Correct answer:

$\small 2x+4y=7$

Explanation:

The standard form of a line is $\small Ax+By=C$ , where all constants are integers, i.e. whole numbers.

Therefore, the equation written in standard form is $\small 2x+4y=7$ .

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Example Question #2 : Standard Form

Line

Refer to the above red line. What is its equation in standard form?

Possible Answers:

2x+ y = 8

2x - y = 8

2x+ y = -8

2x - y = -8

Correct answer:

2x - y = -8

Explanation:

First, we need to find the slope of the above line.

Given two points, $(x_{1}, y_{1}), (x_{2}, y_{2})$ , the slope can be calculated using the following formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

Second, we note that the -intercept is the point (0,8) .

Therefore, in the slope-intercept form of a line, we can set m = 2 and b = 8 :

y = mx+b

y = 2x+8

Since we are looking for standard form - that is, Ax+By = C - we do the following:

y - y - 8 = 2x+8 - y - 8

-8 = 2x -y

2x - y = -8

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Example Question #3 : Standard Form

Write the following equation in standard form:

y=-3x+2

Possible Answers:

y=-3x+2

3x+y-2=0

3x+y=2

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

Correct answer:

3x+y=2

Explanation:

Standard form of an equation is

Ax+By=C .

Rearrange the given equation to make it look like the above equation as follows:

y=-3x+2

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

y+3x=2

3x+y=2

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Example Question #4 : Standard Form

Rewrite the following equation in standard form.

2+4y=3x+10

Possible Answers:

$x=\frac{4}{3}y-\frac{8}{3}$

4y=3x+8

3x-4y=-8

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

6y=13x

Correct answer:

3x-4y=-8

Explanation:

The standard form of a line is Ax+By=C , where $A, B, \textup{and}\textup{ } C$ are integers.

We therefore need to rewrite 2+4y=3x+10 so it looks like Ax+By=C .

The steps to do this are below:

$2+4y=3x+10 \textup{ (subtract 10 from both sides)}$

$-8 +4y=3x\textup{ (subtract 4y from both sides)}$

$-8=3x-4y\ (\textup{flip the two sides of the equality})$

3x-4y=-8

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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

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

-3x+y =8

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 = 20

3x-y = 16

-3x+y = 16

-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 #5 : Standard Form

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

Possible Answers:

9x-y = -7

9x-y = 7

9x-7y = -1

9x-y = -1

-9x-y = 7

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 #8 : 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+3y = -11

-2x+y = -11

-2x+y = -22

2x-2y = -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 #53 : Linear Algebra

Which of the following is NOT in standard form?

Possible Answers:

15x-y=15

y=5x^2-3x+5

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

y-2=3(x+9)

-19x+y = 3

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 #10 : Standard Form

Write the following equation in standard form.

y-2 = 3(x-3)

Possible Answers:

3x-y = -7

-3x+y = -7

x-3y = -7

3x-y = -11

3x+2y =8

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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GED Math : Standard Form

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Standard Form

Example Question #2 : Standard Form

Example Question #3 : Standard Form

Example Question #4 : Standard Form

Example Question #5 : Standard Form

Example Question #6 : Standard Form

Example Question #5 : Standard Form

Example Question #8 : Standard Form

Example Question #53 : Linear Algebra

Example Question #10 : Standard Form

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