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GED Math : Standard Form

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Example Question #21 : Standard Form

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+y =-9

-7x+y =-19

-7x+2y =-5

7x-3y =-5

-7x+y =-6

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 #238 : Algebra

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

Possible Answers:

-x+4y = -8

-8x+4y = -1

-4x+y =2

-4x+y = -2

-4x+y = -8

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 #239 : Algebra

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 #21 : Standard Form

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:

4x+ 14y = 1

14x- 4y = 1

14x+4y = 1

4x-14y =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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Example Question #71 : Linear Algebra

What is the standard form of the equation of the line that goes through the point (5, 2) and has a slope of ?

Possible Answers:

4x+y=8

4x+y=-8

$x+\frac{1}{4}y=8$

4x-y=18

Correct answer:

4x-y=18

Explanation:

Start by writing out the equation of the line in point-slope form.

y-2=4(x-5)

Simplify this equation.

y-2=4x-20

Now, recall what the standard form of a linear equation looks like:

Ax+By=C , where $A, B, \text{ and }C$ are integers. Traditionally, is positive.

Rearrange the equation found from the point-slope form so that it has the and terms on one side, and a number on the other side.

y-2=4x-20

y-2-4x=-20

-4x+y=-18

Since the term should be positive, multiply the entire equation by .

4x-y=18

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GED Math : Standard Form

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Standard Form

Example Question #238 : Algebra

Example Question #239 : Algebra

Example Question #21 : Standard Form

Example Question #71 : Linear Algebra

All GED Math Resources

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