SAT Math - Parallel Lines

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?

$y=-\frac{3}{4}x+2.75$

$y=-\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.75$

$y=\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.625$

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

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?

$y=-\frac{3}{4}x+2.75$

$y=-\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.75$

$y=\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.625$

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

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?

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.

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?

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.

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.

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.

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

$y = \frac{-5}{3}x + 6$

$y = \frac{3}{5}x - 2$

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

$y = \frac{-2}{3}x + 5$

$y = \frac{3}{2}x - 4$

Explanation

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

$y = \frac{-5}{3}x + \frac{8}{3}$

For parallel lines, the slopes must be equal, so the slope of the new line must also be $\frac{-5}{3}$ . 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.

$-4 = \frac{-5}{3}(6) + b$

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

$y = \frac{-5}{3}x + 6$

Which of the following are parallel to the line ?

C. $y=-\frac{1}{2}x+2$

E. $y=-\frac{1}{2}x +6$

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.