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Algebra 1 : How to write expressions and equations

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Example Questions

Example Question #921 : Algebra 1

Equations of a line can be represented as follows:

(1) ax+by=c (standard form)

(2) y=mx+b (slope-intercept form)

(3) $\left ( y-y_{1} \right ) = m\left ( x-x_{1} \right )$ (point-slope form)

Possible Answers:

none of the above

Correct answer:

Explanation:

The equation of line is

y=3

Hence

rise = 0

and the

slope=0

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Example Question #922 : Algebra 1

Find the equation of a line parallel to

y = -3x -3

and passes through $\left ( 2,1 \right )$ .

Possible Answers:

y = -3x +b

y = -3x -7

y = -3x +7

y = 3x + 7

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

Correct answer:

y = -3x +7

Explanation:

The equation of a line parallel to the given line must be of the form:

y = -3x + b

Since the line passes through $\left ( 2,1 \right )$ ,

we can calculate by replacing with 2 and with 1 which gives us the following

$1 = -3\left ( 2 \right ) + b$

Solving for gives us the following equation

y = -3x + 7

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Example Question #923 : Algebra 1

Find the equation of a line perpendicular to

y = -3x -3

and passes through $\left ( 2,1 \right )$

Possible Answers:

y = -3x + 7

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

y = 3x + 3

$y = \frac{1}{3}x$

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

Correct answer:

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

Explanation:

The slope of a line perpendicular to

y = -3x - 3

which has a slope of , is the negative reciprocal of .

Hence we get

$y = \frac{1}{3}x + b$

Replacing and with the given point we get

$1 = \frac{1}{3}\left ( 2 \right ) + b$

Solving for we get

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

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Example Question #11 : How To Write Expressions And Equations

Find the equation of a line perpendicular to

y = 3

and passes through $\left ( -2, 2 \right )$

Possible Answers:

$y = \frac{1}{3}x$

x = 2

x = -2

y = 2

y = 2x

Correct answer:

x = -2

Explanation:

Any line perpendicular to y = 3 ,

which is a horizontal line, must be a vertical line.

Since it passes through the point $\left ( -2, 2 \right )$ and must be perpendicular to

y = 3

The equation must be

x = -2

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Example Question #11 : How To Write Expressions And Equations

Solve by substitution method:

2x - y = 2

x + 2y = -5

Possible Answers:

$\left ( 3, 4 \right )$

$\left ( -3, -4 \right )$

$\left ( 4, 3 \right )$

$\left ( 3, -4 \right )$

$\left ( -3, 4 \right )$

Correct answer:

$\left ( 3, 4 \right )$

Explanation:

From the second equation and by solving for in terms of we get

x = -5 + 2y

Replacing in the first equation with

x = -5 + 2y

we get $2\left ( -5 + 2y \right ) - y = 2$

Solving for one gets y = 4

Replacing with 4 in the above equation:

$-5 + 2\left ( 4 \right )=3$

Hence the solution to the above system of linear equations is $\left ( 3, 4 \right )$ .

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Example Question #12 : How To Write Expressions And Equations

Solve the following system of linear equations by the elimination method:

x - 3y = 3

3x + 2y = -2

Possible Answers:

$\left ( 1, -1 \right )$

$\left ( 0, -1 \right )$

$\left ( 1, 0 \right )$

$\left ( -1, 0 \right )$

$\left ( 0, 1 \right )$

Correct answer:

$\left ( 0, -1 \right )$

Explanation:

We would like to eliminate .

Hence we multiply the first equation by which gives us the following equations:

- 3x +9y = -9

3x + 2y = -2

Adding the above two equations eliminates the variable . We are left with:

11y = -11

and so y=1

Replacing with y=-1 in the original equation gives us

$x - 3\left ( -1 \right ) = 3$

solving for gives us

x = 0

Hence the solution is $\left ( 0, -1 \right )$ .

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Example Question #11 : How To Write Expressions And Equations

For the following two linear equations determine whether the two lines are __________:

-3x + 2y = -1

6x -4y = 2

(1) parallel

(2) perpendicular

(3) neither

(4) dependent

Possible Answers:

Dependent

Perpendicular

None of the above

Neither

Parallel

Correct answer:

Dependent

Explanation:

These two equations represent the same line and they "cross' at infinitely many points. Therefore these systems are dependent.

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Example Question #12 : How To Write Expressions And Equations

$\fn_cm Simplify \; x^{3} + 3x^{2} - 6x + 10 -(x^{2} +x + 13)$

Possible Answers:

-3-5x+2x^2 +x^3

23-5x+2x^2+x^3

$\fn_cm -3-7x+2x^2+x^3$

23-7x+2x^2+x^3

Correct answer:

$\fn_cm -3-7x+2x^2+x^3$

Explanation:

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Example Question #12 : How To Write Expressions And Equations

Which of the following sentences translates to the algebraic equation 8 (x-3) = 40 ?

Possible Answers:

The product of eight and a number subtracted from three is equal to forty.

Eight multiplied by the difference of a number and three is equal to forty.

Three subtracted from the product of eight and a number is equal to forty.

The product of three and a number less eight is equal to forty.

Eight multiplied by the difference of three and a number is equal to forty.

Correct answer:

Eight multiplied by the difference of a number and three is equal to forty.

Explanation:

The expression on the left shows eight being multiplied by an expression in parentheses; that expression is the difference of an unknown number and three. The whole right expression is therefore worded as "Eight multiplied by the difference of a number and three"; the equality symbol and the forty round out the answer.

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Example Question #13 : How To Write Expressions And Equations

Which of the following sentences translates to the equation $\frac{x-9}{5} = 80$ ?

Possible Answers:

Five divided by the difference of a number and nine is equal to eighty.

Nine subtracted from the quotient of a number and five is equal to eighty.

Nine divided by the difference of a number and five is equal to eighty.

Five subtracted from the quotient of a number and nine is equal to eighty.

Five divided into the difference of a number and nine is equal to eighty.

Correct answer:

Five divided into the difference of a number and nine is equal to eighty.

Explanation:

x-9 can be written as "the difference of a number and nine"; the expression on the left shows that difference being divided by five, or, alternatively stated, "five divided into the difference of a number and nine". "Is equal to eighty " rounds out the sentence.

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Algebra 1 : How to write expressions and equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #921 : Algebra 1

Example Question #922 : Algebra 1

Example Question #923 : Algebra 1

Example Question #11 : How To Write Expressions And Equations

Example Question #11 : How To Write Expressions And Equations

Example Question #12 : How To Write Expressions And Equations

Example Question #11 : How To Write Expressions And Equations

Example Question #12 : How To Write Expressions And Equations

Example Question #12 : How To Write Expressions And Equations

Example Question #13 : How To Write Expressions And Equations

All Algebra 1 Resources

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