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Write the equation of the following line in the form y equals m x plus c

To find the equation of the line in the form \( y = mx + c \) (where \( m \) is the slope and \( c \) is the y-intercept), let's extract the necessary information from the graph.

### Step 1: Identify two points on the line
From the graph, we can select two clear points that the line passes through:
- Point \( A \) at \( (0, 4) \)
- Point \( B \) at \( (4, 0) \)

### Step 2: Calculate the slope \( m \)
The slope \( m \) is given by the formula:

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

For points \( A(0, 4) \) and \( B(4, 0) \):

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

So, the slope \( m = -1 \).

### Step 3: Find the y-intercept \( c \)
The y-intercept is the value of \( y \) when \( x = 0 \). From the graph, we can see that when \( x = 0 \), \( y = 4 \). Therefore, \( c = 4 \).

### Step 4: Write the equation
Now that we have the slope \( m = -1 \) and the y-intercept \( c = 4 \), the equation of the line is:

\[
y = -x + 4
\]

Would you like more details or have any questions on this?

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Here are some questions to extend this:

1. How do you calculate the slope if the line is vertical or horizontal?
2. What happens to the equation of a line when the slope is 0?
3. Can you rewrite the equation in general form \( Ax + By + C = 0 \)?
4. How do you interpret the slope and y-intercept in real-world situations?
5. What effect does changing the slope \( m \) have on the steepness of the line?

**Tip:** The slope of a line indicates its steepness and direction. A negative slope means the line is sloping downwards as you move from left to right.

Write the equation of the following line in the form y = mx + c

Learn how to write the equation of a line from a graph using the slope-intercept form y = mx + c. In this example, we find the slope and y-intercept of the line using two points and write the equation. Suitable for students in Grades 8-10.

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