### All GRE Math Resources

## Example Questions

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

What is the equation of the straight line passing through (–2, 5) with an x-intercept of 3?

**Possible Answers:**

y = –5x + 3

y = –x – 3

y = –5x – 3

y = –x + 3

**Correct answer:**

y = –x + 3

First you must figure out what point has an x-intercept of 3. This means the line crosses the x-axis at 3 and has no rise or fall on the y-axis which is equivalent to (3, 0). Now you use the formula (y_{2 }–_{ }y_{1})/(x_{2 }– x_{1}) to determine the slope of the line which is (5 – 0)/(–2 – 3) or –1. Now substitute a point known on the line (such as (–2, 5) or (3, 0)) to determine the y-intercept of the equation y = –x + b. b = 3 so the entire equation is y = –x + 3.

### Example Question #51 : Lines

What is the equation of the line passing through (–1,5) and the upper-right corner of a square with a center at the origin and a perimeter of 22?

**Possible Answers:**

y = (–1/5)x + 2.75

y = (–3/5)x + 28/5

y = (–3/5)x + 22/5

y = –x + 5

y = (3/5)x + 22/5

**Correct answer:**

y = (–3/5)x + 22/5

If the square has a perimeter of 22, each side is 22/4 or 5.5. This means that the upper-right corner is (2.75, 2.75)—remember that each side will be "split in half" by the x and y axes.

Using the two points we have, we can ascertain our line's equation by using the point-slope formula. Let us first get our slope:

m = rise/run = (2.75 – 5)/(2.75 + 1) = –2.25/3.75 = –(9/4)/(15/4) = –9/15 = –3/5.

The point-slope form is: y – y_{0} = m(x – x_{0}). Based on our data this is: y – 5 = (–3/5)(x + 1); Simplifying, we get: y = (–3/5)x – (3/5) + 5; y = (–3/5)x + 22/5

### Example Question #51 : Coordinate Geometry

What is the equation of a line passing through the points and ?

**Possible Answers:**

**Correct answer:**

Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:

Now, for a point and a slope , the point-slope form of a line is:

Let's use for our point

This gives us:

Now, distribute and solve for :

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

What is the equation of a line passing through the two points and ?

**Possible Answers:**

**Correct answer:**

Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:

Now, for a point and a slope , the point-slope form of a line is:

Let's use for our point

This gives us:

Now, distribute and solve for :

### Example Question #31 : Other Lines

What is the equation of a line passing through with a -intercept of ?

**Possible Answers:**

**Correct answer:**

Based on the information that you have been provided, you can quickly find the slope of your line. Since the y-intercept is , you know that the line contains the point . Therefore, the slope of the line is found:

Based on this information, you can use the standard slope-intercept form to find your equation:

, where and

### Example Question #1 : Other Lines

Given the graph of the line below, find the equation of the line.

**Possible Answers:**

**Correct answer:**

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

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

Which line passes through the points (0, 6) and (4, 0)?

**Possible Answers:**

y = –3/2x + 6

y = 2/3 + 5

y = 1/5x + 3

y = –3/2 – 3

y = 2/3x –6

**Correct answer:**

y = –3/2x + 6

P_{1} (0, 6) and P_{2} (4, 0)

First, calculate the slope: m = rise ÷ run = (y_{2} – y_{1})/(x_{2 }– x_{1}), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

### Example Question #55 : Geometry

What line goes through the points (1, 3) and (3, 6)?

**Possible Answers:**

4x – 5y = 4

–2x + 2y = 3

2x – 3y = 5

–3x + 2y = 3

3x + 5y = 2

**Correct answer:**

–3x + 2y = 3

If P_{1}(1, 3) and P_{2}(3, 6), then calculate the slope by m = rise/run = (y_{2} – y_{1})/(x_{2} – x_{1}) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

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

What is the slope-intercept form of ?

**Possible Answers:**

**Correct answer:**

The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate on the left side:

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

A line is defined by the following equation:

What is the slope of that line?

**Possible Answers:**

**Correct answer:**

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4