### All Intermediate Geometry Resources

## Example Questions

### Example Question #1 : Coordinate Geometry

What is the equation of a line that is parallel to the line and includes the point ?

**Possible Answers:**

**Correct answer:**

The line parallel to must have a slope of , giving us the equation . To solve for *b*, we can substitute the values for *y* and *x*.

Therefore, the equation of the line is .

### Example Question #21 : Parallel Lines

Suppose a line . What is the equation of a parallel line that intersects point ?

**Possible Answers:**

**Correct answer:**

A line parallel to must have a slope of two. Given the point and the slope, use the slope-intercept formula to determine the -intercept by plugging in the values of the point and solving for :

Plug the slope and the -intercept into the slope-intercept formula:

### Example Question #31 : Parallel Lines

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

**Possible Answers:**

**Correct answer:**

Write in slope intercept form, , to determine the slope, :

The slope is:

Given the slope, use the point and the equation to solve for the value of the -intercept, . Substitute the known values.

With the known slope and the -intercept, plug both values back to the slope intercept formula. The answer is .

### Example Question #32 : Parallel Lines

Given , find the equation of a line parallel.

**Possible Answers:**

**Correct answer:**

The definition of a parallel line is that the lines have the same slopes, but different intercepts. The only answer with the same slope is .

### Example Question #33 : Parallel Lines

Which one of these equations is parallel to:

**Possible Answers:**

**Correct answer:**

Equations that are parallel have the same slope.

For the equation:

The slope is since that is how much changes with increment of .

The only other equation with a slope of is:

### Example Question #34 : Parallel Lines

What equation is parallel to:

**Possible Answers:**

**Correct answer:**

To find a parallel line to

we need to find another equation with the same slope of or .

The only equation that satisfies this is .

### Example Question #35 : Parallel Lines

What equation is parallel to:

**Possible Answers:**

**Correct answer:**

To find an equation that is parallel to

we need to find an equation with the same slope of .

Basically we are looking for another equation with .

The only other equation that satisfies this is

.

### Example Question #36 : Parallel Lines

A line is parallel to the line of the equation

and passes through the point .

Give the equation of the line in standard form.

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

Two parallel lines have the same slope. Therefore, it is necessary to find the slope of the line of the equation

Rewrite the equation in slope-intercept form . , the coefficient of , will be the slope of the line.

Add to both sides:

Multiply both sides by , distributing on the right:

The slope of this line is . The slope of the first line will be the same. The slope-intercept form of the equation of this line will be

.

To find , set and and solve:

Subtract from both sides:

The slope-intercept form of the equation is

To rewrite in standard form with integer coefficients:

Multiply both sides by 7:

Add to both sides:

,

the correct equation in standard form.

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