### All Algebra 1 Resources

## Example Questions

### Example Question #11 : How To Find The Equation Of A Parallel Line

A line parallel to passes through the points and . Find the equation of this line.

**Possible Answers:**

**Correct answer:**

This problem can be easily solved through using the point-slope formula:

where is the slope and and signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is *parallel to **. *By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation: . Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation.

Here, we arbitrarily choose the point .

### Example Question #12 : How To Find The Equation Of A Parallel Line

A line that passes through the points and is parallel to a line that has a slope of . What is the equation of this line?

**Possible Answers:**

**Correct answer:**

This problem can be easily solved through using the point-slope formula:

where is the slope and and signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is *parallel to a line with a slope of **. *By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation:. Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation.

Here, we arbitrarily choose the point .

### Example Question #13 : How To Find The Equation Of A Parallel Line

A line parallel to passes through the points and . Find the equation for this line.

**Possible Answers:**

**Correct answer:**

This problem can be easily solved through using the point-slope formula:

where is the slope and and signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is **parallel to **. * *By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation: . Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation.

Here, we arbitrarily choose the point .

### Example Question #11 : How To Find The Equation Of A Parallel Line

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

**Possible Answers:**

**Correct answer:**

The first thing we need to do is determine the slope of this parallel line. Recall that parallel lines have the same slope, so the slope of this new line must be .

Next, we must determine the -intercept of the line. The equation for a line is given to us by , and here we know three of the four variables in this new line: .

So when we plug in these numbers we get

Multiply to get:

Subtract from both sides to get:

Therefore, the equation for the line is:

### Example Question #11 : Parallel Lines

If is parallel to and passes through the point , what is the equation of ?

**Possible Answers:**

**Correct answer:**

If f(x) is parallel to g(x) and passes through the point (-4,8), what is the equation of f(x)?

If f(x) is parallel to g(x), then it must have the same slope.

So,

We also know that f(x) goes through the point (-4,8)... Set up the following:

Where b is our y-intercept, which we need to solve for:

Finally, put it all together:

### Example Question #16 : How To Find The Equation Of A Parallel Line

Find the line that is parallel to

and contains the point .

**Possible Answers:**

**Correct answer:**

When finding a line that is parallel to another line, we know that the slopes must be the same. So in the equation,

we know it has a slope of 2. We also know the parallel line contains the point

(-1, 5)

So, we will substitute the slope as well as the point into the y-intercept formula:

Doing this, we will find *b*, or the y-intercept, and we can determine the line that is parallel.

Now, we know the slope of the parallel line is still 2, and now we know the y-intercept is 7. Knowing this, we get the line

.

Therefore, is parallel to .

### Example Question #11 : How To Find The Equation Of A Parallel Line

Which of the following equations will be parallel to the line connected to the points and ?

**Possible Answers:**

**Correct answer:**

In order to determine the equation, we will need to find the slope of the line connected by the two given points.

Use the slope formula to determine the slope.

Substitute the points.

Our equation parallel this line connected by the two points must have a slope of negative one-half.

The only answer that has that slope is:

### Example Question #12 : Parallel Lines

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

**Possible Answers:**

**Correct answer:**

When finding the slope of a parallel line, we need to ensure we have form. stands for slope. Our is which is also the slope of the parallel line. Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Subtract on both sides.

Our equation is .

### Example Question #19 : How To Find The Equation Of A Parallel Line

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

**Possible Answers:**

**Correct answer:**

When finding the slope of a parallel line, we need to ensure we have form. By subtracting on both sides and dividing on both sides, we get

.

stands for slope. Our is or which is also the slope of the parallel line. Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Subtract on both sides.

Our equation is

.

### Example Question #20 : How To Find The Equation Of A Parallel Line

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

**Possible Answers:**

**Correct answer:**

When finding the slope of a parallel line, we need to ensure we have form. By dividing on both sides, we get

.

stands for slope. Our is or which is also the slope of the parallel line. Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Add on both sides.

Our equation is

.

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