# Algebra 1 : How to find the equation of a parallel line

## Example Questions

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### Example Question #1 : How To Find The Equation Of A Parallel Line

Find a line parallel to

Explanation:

A parallel line will have the same  value, in this case , as the orignal line but will intercept the  at a different location.

### Example Question #2 : How To Find The Equation Of A Parallel Line

Which of the following lines are parallel to the line defined by the equation:

Explanation:

Parallel means the same slope:

Solve for :

Find the linear equation where

.

### Example Question #3 : How To Find The Equation Of A Parallel Line

What is the equation of the line parallel to   that passes through (1,1)?

Explanation:

The line parallel to will have the same slope.

The equation for our parallel line will be:

Using the point (1,1) we can solve for the y-intercept:

### Example Question #4 : How To Find The Equation Of A Parallel Line

Which of these lines is parallel to ?

Explanation:

Parallel lines have identical slopes. If you convert the given equation to the form , it becomes

The slope of this equation is , so its parallel line must also have a slope of . The only other line with a slope of  is

### Example Question #5 : How To Find The Equation Of A Parallel Line

Which of these lines is parallel to

None of the other answers are correct.

Explanation:

Parallel lines have identical slopes. To determine the slope of the given line, convert it to  form:

2y = 3x + 8

This line has a slope of .

The only answer choice with a slope of  is .

### Example Question #6 : How To Find The Equation Of A Parallel Line

Choose which of the four equations listed is parallel to the given equation.

Explanation:

is the correct answer because when each term is divided by 2 in order to see the equation in terms of y, the slope of the equation is , which is the same as the slope in the given equation. Parallel lines have the same slope.

### Example Question #7 : How To Find The Equation Of A Parallel Line

Write an equation for a line that is parallel to  and has a y-intercept of

Explanation:

The equation of a line can be written using the expression  where  is the slope and  is the y-intercept. When lines are parallel to each other, it means that they have the same slope, so . The y-intercept is given in the problem as . This means that the equation would be .

### Example Question #8 : How To Find The Equation Of A Parallel Line

Write the equation for a line parallel to passing through the point .

Explanation:

In order to approach this problem, we need to be familiar with the slope-intercept equation of a line, where m is the slope and b is the y-intercept. The line that our line is supposed to be parallel to is . Lines that are parallel have the same slope, m, so the slope of our new line is . Since we don't know the y-intercept yet, for now we'll write our equation as just:

. We can solve for b using the point we know the line passes though, . We can plug in 4 for x and -2 for y to solve for b:

first we'll multiply to get 1:

now we can subtract 1 from both sides to solve for b:

Now we can just go back to our equation and sub in -3 for b:

### Example Question #9 : How To Find The Equation Of A Parallel Line

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

A line cannot pass through this point and be parallel to the original line.

None of the other answers.

None of the other answers.

Explanation:

Parallel lines have the same slope. So our line should have a slope of 2x. Next we use the point slope formula to find the equation of the line that passes through  and is parallel to .

Point slope formula:

is the slope of the line parallel to  which passes through .

### Example Question #10 : How To Find The Equation Of A Parallel Line

Find the equation of the line parallel to the given criteria:  and that passes through the point