SAT Math - How to find the equation of a parallel line

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

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.

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

What line is parallel to at ?

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

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

$y=-\frac{3}{2}x+8$

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

None of the answers are correct

Explanation

Find the slope of the given line: (slope intercept form)

$y=\frac{-2}{3}x+2$ therefore the slope is $\frac{-2}{3}$

Parallel lines have the same slope, so now we need to find the equation of a line with slope $\frac{-2}{3}$ and going through point by substituting values into the point-slope formula.

$2=\frac{-2}{3}(3)+b$

So,

Thus, the new equation is $y=\frac{-2}{3}x+4$

Which of the following equations is parallel to: $y=\frac {2}{3}x+4$ and goes through the point ?

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

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

Explanation

Step 1: We need to define what a parallel line is. A parallel line has the same slope as the line given in the problem. Parallel lines never intersect, which tells us that the y-intercepts of the two equations are different.

Step 2: We need to identify the slope of the line given to us. The slope is always located in front of the .

The slope in the equation is $\frac {2}{3}$ .

Step 3: If we said that a parallel line has the same slope as the given line in the equation, the slope of the parallel equation is also $\frac {2}{3}$ .

Step 4. We need to write the equation of the parallel line in slope-intercept form:. We need to write b for the intercept because it has changed.

The equation is: $y=\frac {2}{3}x+b$

Step 5: We will use the point where and . We need to substitute these values of x and y into the equation in step 4 and find the value of b.

$y=\frac {2}{3}x+b$
$5=\frac {2}{3}*3+b$
$5=\frac {2}{{\color{Red} 3}}*{\color{Red} 3}+b$
The numbers in red will cancel out when I multiply.

To find b, subtract 2 to the other side

Step 6: We put all of the parts together and make the final equation of the parallel line:

The final equation is: $y=\frac {2}{3}x+3$

What line is parallel to 2x + 5y = 6 through (5, 3)?

y = 5/2x + 3

y = 3/5x – 2

y = –2/5x + 5

y = 5/3x – 5

y = –2/3x + 3

Explanation

The given equation is in standard form and needs to be converted to slope-intercept form which gives y = –2/5x + 6/5. The parallel line will have a slope of –2/5 (the same slope as the old line). The slope and the given point are substituted back into the slope-intercept form to yield y = –2/5x +5.

What line is parallel to through ?

Explanation

The slope of the given line is and a parallel line would have the same slope, so we need to find a line through with a slope of 2 by using the slope-intercept form of the equation for a line. The resulting line is which needs to be converted to the standard form to get .

If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2_x_ – 3, what is the value of p ?

_–_10

_–_17

Explanation

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (_–2–_5) must equal _–_2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p.

$\frac{p--3}{-2-5}=\frac{p+3}{-2-5}=-2$

$\frac{p+3}{-7}=-2$

$(\frac{p+3}{-7})-7=-2(-7)$

Which of the following is the equation of a line that is parallel to the line 4_x_ – y = 22 and passes through the origin?

y – 4_x_ = 22

(1/4)x + y = 0

4_x_ + 8_y_ = 0

4_x_ – y = 0

4_x_ = 8_y_

Explanation

We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4_x_ – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.

In 4_x_ – y = 0 we can rearrange to get y = 4_x_. This fulfills both requirements.

What line is parallel to and passes through the point ?

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

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

$y = \frac{1}{3}x + 6$

$y = \frac{-1}{3}x - 5$

Explanation

Start by converting the original equation to slop-intercept form.

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

The slope of this line is $-\frac{3}{2}$ . A parallel line will have the same slope. Now that we know the slope of our new line, we can use slope-intercept form and the given point to solve for the y-intercept.

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

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

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

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

What is the equation of a line that is parallel to and passes through ?

$y=\frac{5}{6}x-10$

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

$y=-\frac{3}{5}x+10$

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

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

Explanation

To solve, we will need to find the slope of the line. We know that it is parallel to the line given by the equation, meaning that the two lines will have equal slopes. Find the slope of the given line by converting the equation to slope-intercept form.

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

The slope of the line will be $-\frac{3}{5}$ . In slope intercept-form, we know that the line will be $y=-\frac{3}{5}x+b$ . Now we can use the given point to find the y-intercept.