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GED Math : Algebra

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Example Questions

Example Question #61 : Linear Algebra

Line

Give the equation, in standard form, of the line on the above set of coordinate axes.

Possible Answers:

5x-3y = 15

5x+3y = 15

3x-5y = 15

3x+ 5y = 15

Correct answer:

5x+3y = 15

Explanation:

The -intercept of the line can be seen to be at the point five units above the origin, which is (0, 5) . The -intercept is at the point three units to the right of the origin, which is (3,0) . From these intercepts, we can find slope by setting b= 5,a = 3 in the formula

$m = - \frac{b}{a}$

The slope is

$m = - \frac{5}{3}$

Now, we can find the slope-intercept form of the line

y = mx + b

By setting $m = - \frac{5}{3}$ , b= 5 :

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

The standard form of a linear equation in two variables is

ax+by = c ,

so in order to find the equation in this form, first, add $- \frac{5}{3}x$ to both sides:

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

$\frac{5}{3}x+ y = 5$

We can eliminate the fraction by multiplying both sides by 3:

$3 \left (\frac{5}{3}x+ y \right )= 3 \cdot 5$

Distribute by multiplying:

$3 \cdot \frac{5}{3}x+3 \cdot y =15$

5x+3y = 15 ,

the correct equation.

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Example Question #61 : Linear Algebra

Write the given equation in standard form: 3+y =2(2x-6)

Possible Answers:

-4x+y = 9

4x-2y =9

4x+y = 15

-4x+y = -15

4x+y=-9

Correct answer:

-4x+y = -15

Explanation:

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

Simplify the right side by distribution.

3+y =2(2x)-(2)(6)

y+3 = 4x-12

Subtract on both sides.

y+3 -4x= 4x-12-4x

The equation becomes:

-4x+y+3 = -12

Subtract 3 from both sides.

-4x+y+3-3 = -12-3

The answer is: -4x+y = -15

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Example Question #11 : Standard Form

Given the point (1,3) with a slope of two, write the equation in standard form.

Possible Answers:

y=2x-1

-2x-2y = 1

-2x+y = 1

2x-3y =-1

2x+3y =-1

Correct answer:

-2x+y = 1

Explanation:

We will first need to write the point-slope form to set up the equation.

y-y_1 = m(x-x_1)

Substitute the slope and point.

y-3= 2(x-1)

Simplify the right side.

y-3 = 2x-2

Add 3 on both sides.

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

y=2x+1

Subtract on both sides.

y-2x=2x+1-2x

The answer is: -2x+y = 1

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Example Question #12 : Standard Form

Find the equation in standard form: y=4(x-4)

Possible Answers:

2x+y = -4

-2x+y = -8

-4x+y = -4

-4x+y = -16

2x+y = -16

Correct answer:

-4x+y = -16

Explanation:

Distribute the right side.

y=4x-16

Subtract on both sides.

y-4x=4x-16-4x

The answer is: -4x+y = -16

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Example Question #19 : Standard Form

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

Possible Answers:

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

4x-4y =-6

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

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

4x+4y =-6

Correct answer:

4x-4y =-6

Explanation:

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

Multiply by two on both sides to eliminate the fraction.

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

x= 4x-4y+6

Subtract on both sides.

x-x= 4x-4y+6-x

0 = 4x-4y +6

Subtract 6 from both sides.

The answer is: 4x-4y =-6

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Example Question #20 : Standard Form

Given the slope is 3, and the y-intercept is 6, write the equation of the line in standard form.

Possible Answers:

3x-y= 6

x+3y=6

-3x+y= 6

3x+y= 6

x-3y=6

Correct answer:

-3x+y= 6

Explanation:

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

First, we can write the equation in slope-intercept form: y=mx+b

y=3x+6

Subtract on both sides.

y-3x=3x+6-3x

The answer is: -3x+y= 6

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Example Question #62 : Linear Algebra

Given the slope of a line is 7, and a known point is (2,5), what is the equation of the line in standard form?

Possible Answers:

7x-3y =-5

-7x+y =-6

-7x+2y =-5

-7x+y =-19

-7x+y =-9

Correct answer:

-7x+y =-9

Explanation:

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

We can use the point-slope form of a line since we are only given the slope and a point.

y-y_1 = m( x-x_1)

Substitute the slope and the point.

y-5 = 7( x-2)

Simplify this equation.

y-5 = 7x-14

Add on both sides.

y-5+5= 7x-14+5

y=7x-9

Subtract from both sides.

y- 7x=7x-9- 7x

Simplify both sides.

-7x+y =-9

The answer is: -7x+y =-9

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Example Question #63 : Linear Algebra

Rewrite the equation in standard form: y= 4(x-2)

Possible Answers:

-x+4y = -8

-4x+y = -2

-4x+y =2

-4x+y = -8

-8x+4y = -1

Correct answer:

-4x+y = -8

Explanation:

Distribute the four through both terms of the binomial.

y=4x-8

Subtract on both sides of the equation.

y-4x=4x-8-4x

Simplify both sides.

-4x+y = -8

The answer is: -4x+y = -8

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Example Question #22 : Standard Form

Which of the following is an equation, in standard form, of the line of the coordinate plane with intercepts (-3, 0 ) and (0, 8 ) ?

Possible Answers:

8 x + 3 y =-24

8 x + 3 y =24

8 x - 3 y =-24

8 x - 3 y =24

Correct answer:

8 x - 3 y =-24

Explanation:

First, find the slope-intercept form of the equation. This is

y = mx+b ,

where is the slope and (0,b) is the -intercept of the line. Since (0, 8 ) is this intercept, b = 8 . Also, the slope of a line with intercepts (a,0 ) and (0,b) is $m = - \frac{b}{a}$ , so, setting a = -3, b = 8 ,

$m = - \frac{8}{-3} = \frac{8}{3}$ .

The slope-intercept form is

$y = \frac{8}{3} x + 8$

The standard form of the equation is

Ax+By = C ,

where, by custom, , , and are relatively prime integers, and A > 0 . To accomplish this:

Switch the expressions:

$\frac{8}{3} x + 8 = y$

Add -y-8 to both sides:

$\frac{8}{3} x + 8+ (-y-8 ) = y + (-y-8 )$

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

Multiply both sides by 3 to eliminate the denominator and make the coefficients integers with GCF 1:

$3 \cdot \left (\frac{8}{3} x - y \right ) =3 \cdot( -8 )$

Distribute on the left:

$3 \cdot \frac{8}{3} x - 3 \cdot y =3 \cdot( -8 )$

8 x - 3 y =-24

This is the correct equation.

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Example Question #231 : Algebra

Rewrite the equation

$y = \frac{2}{7}x- \frac{1}{14}$

in standard form so that the coefficients are integers, the coefficient of is positive, and the three integers are relatively prime.

Possible Answers:

14x- 4y = 1

4x-14y =1

4x+ 14y = 1

14x+4y = 1

Correct answer:

4x-14y =1

Explanation:

The standard form of the equation of a line is

ax+ by = c .

To rewrite the equation

$y = \frac{2}{7}x- \frac{1}{14}$

in this form so that has a positive coefficient, first, switch the places of the expressions:

$\frac{2}{7}x- \frac{1}{14} = y$

Get the term on the left and the constant on the right by adding $-y+ \frac{1}{14}$ to both sides:

$\frac{2}{7}x- \frac{1}{14} + \left ( -y+ \frac{1}{14} \right ) = y+ \left ( -y+ \frac{1}{14} \right )$

$\frac{2}{7}x- y = \frac{1}{14}$

To eliminate fractions and ensure that the coefficients are relatively prime, multiply both sides by lowest common denominator 14:

$14 \cdot \left (\frac{2}{7}x- y \right ) = 14 \cdot \frac{1}{14}$

$14 \left (\frac{2}{7}x- y \right ) = \frac{14}{1} \cdot \frac{1}{14}$

$14 \cdot \left (\frac{2}{7}x- y \right ) =1$

Multiply 14 by both expressions in the parentheses:

$14 \cdot \frac{2}{7}x-14 \cdot y =1$

$\frac{14}{1} \cdot \frac{2}{7}x-14y =1$

Cross-canceling:

$\frac{2}{1} \cdot \frac{2}{1}x-14y =1$

4x-14y =1 ,

the correct choice.

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GED Math : Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #61 : Linear Algebra

Example Question #61 : Linear Algebra

Example Question #11 : Standard Form

Example Question #12 : Standard Form

Example Question #19 : Standard Form

Example Question #20 : Standard Form

Example Question #62 : Linear Algebra

Example Question #63 : Linear Algebra

Example Question #22 : Standard Form

Example Question #231 : Algebra

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