Question

This is a graph with the x-axis labeled from -5 to 5 and the y-axis labeled from -4 to 4.
There is a diagonal line that passes through the following points:
(0, 4) (the y-intercept)
(2, 2)
(4, 0)
The line slopes downward from left to right, indicating a negative slope.

a) What is the slope of the graph?

b) What is the y-intercept?

c) What is the equation of the line?

Answer 1

To find the various characteristics of the line described, let's analyze the information provided.

### a) What is the slope of the graph?
The slope \( m \) can be calculated using two points on the line. We'll use the points (0, 4) and (4, 0).

The formula for the slope \( m \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 4) and (4, 0):
- \( x_1 = 0, y_1 = 4 \)
- \( x_2 = 4, y_2 = 0 \)

Substituting these values into the formula:

\[
m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
\]

So, the slope of the graph is \( -1 \).

### b) What is the y-intercept?
The y-intercept is the point where the line crosses the y-axis. From the given points, we can see that the y-intercept is (0, 4).

So, the y-intercept is \( 4 \).

### c) What is the equation of the line?
The equation of a line in slope-intercept form is given by:

\[
y = mx + b
\]

Where \( m \) is the slope and \( b \) is the y-intercept. We found the slope \( m = -1 \) and the y-intercept \( b = 4 \).

Substituting these values into the equation:

\[
y = -1x + 4
\]

This can be simplified to:

\[
y = -x + 4
\]

Thus, the equation of the line is:

\[
y = -x + 4
\]