Parallel Lines

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SAT Math › Parallel Lines

Questions 1 - 10
1

There is a line defined by the equation below:

There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?

Explanation

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = (3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = (3/4)x + 2.75

2

There is a line defined by the equation below:

There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?

Explanation

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = (3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = (3/4)x + 2.75

3

Assume line a and line b are parallel.

If angle x is three bigger than twice the square of four of angle y, then what is angle y?

5

6

7

8

10

Explanation

The answer is 7.

Line a and b are parallel lines cut by a transverse line which make angle x and y alternate exterior angles. This means that angle x and angle y have the same measurement value.

The square root of 4 is 2; so twice 2 is 4. Then three added to 4 is 7. So x is equal to 7 and thus y is also equal to 7.

4

Assume line a and line b are parallel.

If angle x is three bigger than twice the square of four of angle y, then what is angle y?

5

6

7

8

10

Explanation

The answer is 7.

Line a and b are parallel lines cut by a transverse line which make angle x and y alternate exterior angles. This means that angle x and angle y have the same measurement value.

The square root of 4 is 2; so twice 2 is 4. Then three added to 4 is 7. So x is equal to 7 and thus y is also equal to 7.

5

is parallel to which of the following lines?

Explanation

Remember that when a line is stated as , its slope-intercept conversion has a slope of .

Also bear in mind that we are looking for a parallel line, which means we need to find another line where .

is our answer because , which is what we are looking for.

6

is parallel to which of the following lines?

Explanation

Remember that when a line is stated as , its slope-intercept conversion has a slope of .

Also bear in mind that we are looking for a parallel line, which means we need to find another line where .

is our answer because , which is what we are looking for.

7

What line is parallel to , and passes through the point ?

Explanation

Converting the given line to slope-intercept form we get the following equation:

For parallel lines, the slopes must be equal, so the slope of the new line must also be . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line.

Use the y-intercept in the slope-intercept equation to find the final answer.

8

Which of the following are parallel to the line ?

A.

B.

C.

D.

E.

A & D

A, B, & C

C & D

D & E

None of the given answers

Explanation

In order for two lines to be parallel, they must have the same slope and different y-intercepts. In slope-intercept form, the slope of the coefficient of our value.

We want to find lines that have a slope of . The two answers that share this slope with the given equation are and , which correspond with answers A and D.

9

Which of the following lines is parallel to ?

None of the given answers

Explanation

Remember that in order for two lines to be parallel, their slopes must be the same.

In slope-intercept form, a line's slope is the coefficient of .

For our given line, the slope, therefore, is . The only answer choice whose slope is also is .

Therefore, is the correct answer.

10

What line is parallel to , and passes through the point ?

Explanation

Converting the given line to slope-intercept form we get the following equation:

For parallel lines, the slopes must be equal, so the slope of the new line must also be . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line.

Use the y-intercept in the slope-intercept equation to find the final answer.

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