Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #4001 : Algebra 1

Find the slope of a line parallel to a line with the equation:

Possible Answers:

Correct answer:

Explanation:

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, the slop is .  This is also the slope of the parallel line. 

Example Question #22 : How To Find The Slope Of Parallel Lines

Find the slope of a line parallel to a line with the equation:

Possible Answers:

Correct answer:

Explanation:

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, we need to convert the equation into slope-intercept form.

 

Subtract  from both sides.

 

Divide both sides by .

 

Rewrite.

Identify the slope.

The slope is  or . This is also the slope of the parallel line.

Example Question #22 : How To Find The Slope Of Parallel Lines

Find the slope of a line parallel to a line with the equation:

Possible Answers:

Correct answer:

Explanation:

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, we need to convert the equation into slope-intercept form.

 

Divide both sides by .

 

Identify the slope.

The slope is . This is also the slope of the parallel line.

Example Question #1 : How To Find Out If Lines Are Parallel

Which of the following lines are parallel to y = 2x + 5? 

Possible Answers:

y = –2x + 8

y = 2x – 3

y = (–1/2)x + 6

y = 4x + 3

y = 6x + 5

Correct answer:

y = 2x – 3

Explanation:

Lines are parallel if they have the same slope. The lines are all given in the form y = mx + b. In this form, m represents the slope, thus, we are looking for another line with a slope of 2. This is y = 2x – 3. 

Note that the line given by y = (–1/2)x + 6 has a slope that is the negative reciprocal of 2. This line will be perpendicular to our given line.

Example Question #2 : How To Find Out If Lines Are Parallel

True or False.

The following two lines are parallel.

Possible Answers:

True

False

Correct answer:

True

Explanation:

When both equations are solved for the form  the slopes are the same.

Example Question #3 : How To Find Out If Lines Are Parallel

Which of the following lines are parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines must have identical slopes. The given equation is in the  form. Therefore, we can quickly determine that its slope is 3. The only other equation with a slope of 3 is .

Example Question #4 : How To Find Out If Lines Are Parallel

Which of these lines is parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope. Since all of these equations are in the form, it is easy to determine their slopes, . The slope of is 2.

The only other line with a slope of 2 is .

Example Question #1 : How To Find Out If Lines Are Parallel

Which of these lines is parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines must have equal slopes to one another. Since all of the lines are in the form, it is easy to determine their slopes. The given line has a slope of 3, which means that any line that is parallel to it must have a slope of 3. The only other line with a slope of 3 is .

Example Question #3 : How To Find Out If Lines Are Parallel

Which of these pairs of lines are parallel?

Possible Answers:

none of the other answers

Correct answer:

Explanation:

Parallel lines have the same slope as one another. The only pair of lines with the same slope is .

Example Question #3 : How To Find Out If Lines Are Parallel

Which of these lines is parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have identical slopes with one another. The given line has a slope of 9, so its parallel line must also have a slope of 9. The only other line with a slope of 9 is .

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