### All Intermediate Geometry Resources

## Example Questions

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

Given two points and , find the equation for the line connecting those two points in slope-intercept form.

**Possible Answers:**

**Correct answer:**

If we have two points, we can find the slope of the line between them by using the definition of the slope:

where the triangle is the greek letter 'Delta', and is used as a symbol for 'difference' or 'change in'

Now that we have our slope ( , simplified to ), we can write the equation for slope-intercept form:

where is the slope and is the y-intercept

In order to find the y-intercept, we simply plug in one of the points on our line

So our equation looks like

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

Which of the following is an equation for a line with a slope of and a y-intercept of ?

**Possible Answers:**

**Correct answer:**

Because we have the desired slope and the y-intercept, we can easily write this as an equation in slope-intercept form (y=mx+b).

This gives us . Because this does not match either of the answers in this form (y=mx+b), we must solve the equation for x. Adding 5 to each side gives us . We can then multiple both sides by 3 and divide both sides by 4, giving us .

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

If the -intercept of a line is , and the -intercept is , what is the equation of this line?

**Possible Answers:**

**Correct answer:**

If the y-intercept of a line is , then the -value is when is zero. Write the point:

If the -intercept of a line is , then the -value is when is zero. Write the point:

Use the following formula for slope and the two points to determine the slope:

Use the slope intercept form and one of the points, suppose , to find the equation of the line by substituting in the values of the point and solving for , the -intercept.

Therefore, the equation of this line is .

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

What is the equation of a line that has a slope of and a -intercept of ?

**Possible Answers:**

**Correct answer:**

The slope intercept form can be written as:

where is the slope and is the y-intercept. Plug in the values of the slope and -intercept into the equation.

The correct answer is:

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

What is the equation of a line with a slope of and an -intercept of ?

**Possible Answers:**

**Correct answer:**

The -intercept is the value of when the value is equal to zero. The actual point located on the graph for an -intercept of is . The slope, , is 2.

Write the slope-intercept equation and substitute the point and slope to solve for the -intercept:

Plug the slope and -intercept back in the slope-intercept formula:

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

A line goes through the following points and .

Find the equation of the line.

**Possible Answers:**

**Correct answer:**

First, find the slope of the line using the slope formula:

.

Next we plug one of the points, and the slope, into the point-intercept line forumula:

where m is our slope.

Then and when we plug in point (2,3) the formula reads then solve for b.

.

To find the equation of the line, we plug in our m and b into the slope-intercept equation.

So, or simplified, .

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

Write the equation for the line passing through the points and

**Possible Answers:**

**Correct answer:**

To determine the equation, first find the slope:

We want this equation in slope-intercept form, . We know and because we have two coordinate pairs to choose from representing an and a . We know because that represents the slope. We just need to solve for , and then we can write the equation.

We can choose either point and get the correct answer. Let's choose :

multiply ""

add to both sides

This means that the form is

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

Write the equation for a line that passes through the points and .

**Possible Answers:**

**Correct answer:**

To determine the equation, first find the slope:

We want this equation in slope-intercept form, . We know and because we have two coordinate pairs to choose from representing an and a . We know because that represents the slope. We just need to solve for , and then we can write the equation.

We can choose either point and get the correct answer. Let's choose :

multiply ""

subtract from both sides

This means that the form is

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

Find the equation for a line passing through the points and .

**Possible Answers:**

**Correct answer:**

To determine the equation, first find the slope:

We want this equation in slope-intercept form, . We know and because we have two coordinate pairs to choose from representing an and a . We know because that represents the slope. We just need to solve for , and then we can write the equation.

We can choose either point and get the correct answer. Let's choose :

multiply ""

subtract from both sides

This means that the form is

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

Find the equation for the line passing through the points and .

**Possible Answers:**

**Correct answer:**

To determine the equation, first find the slope:

We can choose either point and get the correct answer. Let's choose :

multiply ""

subtract from both sides

This means that the form is