Algebra 1 : How to write expressions and equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : How To Write Expressions And Equations

Equations of a line can be represented as follows:

(1)  (standard form)

(2)  (slope-intercept form)

(3) (point-slope form)

Possible Answers:

none of the above

Correct answer:

Explanation:

The equation of line  is

Hence 

and the

Example Question #12 : How To Write Expressions And Equations

Find the equation of a line parallel to

and passes through .

Possible Answers:

Correct answer:

Explanation:

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

Since the line passes through ,

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

Solving for  gives us the following equation

Example Question #13 : How To Write Expressions And Equations

Find the equation of a line perpendicular to

and passes through

Possible Answers:

Correct answer:

Explanation:

The slope of a line perpendicular to

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

Hence we get

Replacing  and with the given point we get

 

Solving for  we get

Example Question #14 : How To Write Expressions And Equations

Find the equation of a line perpendicular to

and passes through

Possible Answers:

Correct answer:

Explanation:

Any line perpendicular to ,

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

 

Since it passes through the point and must be perpendicular to

The equation must be

Example Question #11 : How To Write Expressions And Equations

Solve by substitution method:

 

Possible Answers:

Correct answer:

Explanation:

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

Replacing  in the first equation with

we get

Solving for  one gets

 

Replacing  with 4 in the above equation:

Hence the solution to the above system of linear equations is .

Example Question #932 : Algebra 1

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

Possible Answers:

Correct answer:

Explanation:

We would like to eliminate .

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

 

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

and so

Replacing  with  in the original equation gives us

solving for  gives us

Hence the solution is .

Example Question #15 : How To Write Expressions And Equations

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

 

(1) parallel

(2) perpendicular

(3) neither

(4) dependent

Possible Answers:

None of the above

Dependent

Parallel

Perpendicular

Neither

Correct answer:

Dependent

Explanation:

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

Example Question #934 : Algebra 1

 

Possible Answers:

Correct answer:

Explanation:
 



 
 

Example Question #935 : Algebra 1

Which of the following sentences translates to the algebraic equation  ?

Possible Answers:

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

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

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

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

Eight multiplied by the difference of a number and three 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.

Example Question #936 : Algebra 1

Which of the following sentences translates to the equation  ?

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.

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.

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

Correct answer:

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

Explanation:

 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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