# High School Math : Parallel Lines

## Example Questions

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### Example Question #5 : How To Find The Slope Of Parallel Lines

Which of the following equations are parallel to ?

Explanation:

For one equation to be parallel to another, the only requirement is that they must have the same slope. In order to figure out which answer choice is parallel to the given equation, you must first find the slope of the equation:

From the simplified equation, you can see that the slope is .

The answer choice that has the same slope is .

### Example Question #2 : How To Find The Slope Of Parallel Lines

Which of the following is parallel to a line described by

Explanation:

The definition of parallel lines tells us that if two lines are parallel, they have the same slope. Since these lines are described in the slope-intercept form, we know that the slope of these lines are given by the coefficient of the  variable.

The slope in the given equation is 4, so a parallel line would also have a slope of 4. The only answer with this slope is

### Example Question #7 : How To Find The Slope Of Parallel Lines

Which of the following is parallel to the line described by

Explanation:

The definition of parallel lines tells us that if two lines are parallel, they have the same slope. Since these lines are described in the slope-intercept form, we know that the slope of these lines are given by the coefficient of the  variable.

The slope in the given equation is , so a parallel line would also have a slope of . The only answer with this slope is

### Example Question #3 : How To Find The Slope Of Parallel Lines

Which of the following is parallel to the line described by

Explanation:

The definition of parallel lines tells us that if two lines are parallel, they have the same slope. Since these lines are described in the slope-intercept form, we know that the slope of these lines are given by the coefficient of the  variable.

The slope in the given equation is 3, so a parallel line would also have a slope of 3. The only answer with this slope is

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

What line is parallel to through the point ?

Explanation:

The given line can be rewritten as , which has slope .

If the new line is parallel to the old line, it must have the same slope.  So we use the point-slope form of an equation to calculate the new intercept.

becomes where .

So the equation of the parallel line is .

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

Find the equation of a line parallel to

Explanation:

Since parallel lines share the same slope, the only answer that works is

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

Given the equation  and the point , find a line through the point that is parallel to the given line.

Explanation:

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

,

where  represents the slope and  and  represent the given points, plug in the points given and simplify into standard form:

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

What line is parallel to through ?

Explanation:

Parallel lines have the same slopes.  The slope for the given equation is .  We can use the slope and the new point in the slope intercept equation to solve for the intercept:

Therefore the new equation becomes:

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

What line is parallel to through ?

Explanation:

Parallel lines have the same slope.  The slope of the given line is .

Find the line with slope through the point  by plugging this informatuon into the slope intercept equation, :

, which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes , and converting to standard form gives .

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

Find the equation of a line parallel to the line that goes through points  and .