You decide to buy a laptop for $800. In 3 years, the laptop will be worth $450. How much will the computer be worth after 6 years?

Writing a linear equation that relates the two prices will help you determine how much the computer will be worth after 6 years.

### Finding the Equation of a Line

You know how to find the slope between two points. We will now find the entire equation of a line. Recall from Algebra I that the equation of a line in slope-intercept form is

Let's find the equation for the following lines.

- Find the equation of the line below.

Analyze the line. We are given two points on the line, one of which is the

From this, we see that the slope is

Plugging our found information into the slope-intercept equation, the equation of this line is

Alternate Method: If we had used the Slope Formula, we would use (0, 4) and (6, 2), which are the values of the given points.

The slope of a line is -4 and the

This problem explicitly tells us the slope and

- The slope of a line is
12 and it passes through the point (4, -7). What is the equation of the line?

In this problem, we are given

From this, the equation of the line is

We can test if a point is on a line or not by plugging it into the equation. If the equation holds true, the point is on the line. If not, then the point is not on the line.

- Find the equation of the line that passes through (12, 7) and (10, -1).

In this problem, we are not given the slope or the

Now, plug in one of the points for

The equation of the line is

### Examples

#### Example 1

Earlier, you were asked to find how much the computer will be worth after 6 years.

To determine the equation of the line, rewrite the given information as points. The first could be (0, 800) and the second would be (3, 450). We already know that the *y*-intercept is 800 because the *x*-value is zero at that point. Find the slope.

Therefore, the equation of the declining value of the laptop is

#### Example 2

What is the equation of the line where the slope is 1 and passes through (5, 3)?

We are told that

The equation of the line is

#### Example 3

Find the equation of the line that passes through (9, -4) and (-1, -8).

First, find the slope.

Now, find the

The equation of the line is

When your

#### Example 4

Find the equation of the line below.

We can find the slope one of two ways: using slope triangles or by using the Slope Formula. We are given (by the drawn points in the picture) that (-2, 2) and (4, -2) are on the line. Drawing a slope triangle, we have:

We have that the slope is

\begin{align*}2 &= - \frac{2}{3}(-2) + b\\ 2 &= \frac{4}{3} + b \\ \frac{2}{3} &= b\end{align*}

The equation of the line is \begin{align*}y = - \frac{2}{3}x + \frac{2}{3}\end{align*}.

### Review

Find the equation of each line with the given information below.

- slope = 2, \begin{align*}y-\end{align*}intercept = (0, 3)
- \begin{align*}m = -\frac{1}{4}, \ b = 2.6\end{align*}
- slope = -1, \begin{align*}y-\end{align*}intercept = (0, 2)
- \begin{align*}x-\end{align*}intercept = (-2, 0), \begin{align*}y-\end{align*}intercept = (0, -5)
- slope \begin{align*}= \frac{2}{3}\end{align*} and passes through (6, -4)
- slope \begin{align*}= - \frac{3}{4}\end{align*} and passes through (-2, 5)
- slope = -3 and passes through (-1, -7)
- slope = 1 and passes through (2, 4)
- passes through (-5, 4) and (1, 1)
- passes through (5, -1) and (-10, -10)
- passes through (-3, 8) and (6, 5)
- passes through (-4, -21) and (2, 9)

For problems 13-16, find the equation of the lines in the graph below.

- Green Line
- Blue Line
- Red Line
- Purple Line
- Find the equation of the line with zero slope and passes through (8, -3).
- Find the equation of the line with zero slope and passes through the point (-4, 5).
- Find the equation of the line with zero slope and passes through the point \begin{align*}(a, b)\end{align*}.
**Challenge**Find the equation of the line with an*undefined*slope that passes through \begin{align*}(a, b)\end{align*}.

### Answers for Review Problems

To see the Review answers, open this PDF file and look for section 2.2.