How to find the equation of a parallel line

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SSAT Upper Level Quantitative › How to find the equation of a parallel line

Questions 1 - 10
1

Find the equation of a line that goes through the point and is parallel to the line with the equation .

Explanation

For lines to be parallel, they must have the same slope. The slope of the line we are looking for then must be .

The point that's given in the equation is also the y-intercept.

Using these two pieces of information, we know that the equation for the line must be

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

Find the equation of the line that goes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

We can then plug in the given point and the slope into the equation of a line to find the y-intercept.

Now, we can write the equation of the line.

4

Find the equation of the line that passes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Now, we can plug in the point given by the question to find the y-intercept.

From this, we can write the following equation:

5

Find the equation of the line that passes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we know that the equation of the line must be .

6

Find the equation of the line that passes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we know the equation of the line must be .

7

Find the equation of the line that passes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we can write the equation for the line:

8

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.

9

Find the equation of the line that passes through the point and is parallel to the line with the equation .

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we knwo the equation of the line must be .

10

What line is parallel to at ?

None of the answers are correct

Explanation

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

therefore the slope is

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

So,

Thus, the new equation is

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