### All High School Math Resources

## Example Questions

### Example Question #61 : Coordinate Geometry

What line is parallel to through the point ?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 #61 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

Parallel lines share the same slope. Because the slope of the original line is , the correct answer must have that slope, so the correct answer is

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