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To find the equation of the line shown in the graph in the form \( y = mx + c \), we need to determine two things:

1. **Slope (m):** The slope is the change in \( y \) over the change in \( x \) (i.e., "rise over run").
2. **Y-intercept (c):** The point where the line crosses the y-axis.

### Step 1: Determine the Slope (m)
From the graph:
- It passes through the point \((0, 4)\) (where it crosses the y-axis).
- Another point on the line is \((2, 0)\) (where it crosses the x-axis).

The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((0, 4)\) and \((2, 0)\):
\[
m = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2
\]

### Step 2: Find the Y-intercept (c)
The line crosses the y-axis at the point \((0, 4)\), so the y-intercept is:
\[
c = 4
\]

### Step 3: Write the Equation
Substituting \( m = -2 \) and \( c = 4 \) into the equation \( y = mx + c \):
\[
y = -2x + 4
\]

Thus, the equation of the line is:
\[
y = -2x + 4
\]

Would you like more details, or do you have any questions about this?

Here are five related questions:
1. How would the equation change if the line's slope were positive?
2. What is the significance of the y-intercept in this equation?
3. Can you find the equation of a line parallel to this one?
4. How does the slope affect the steepness of the line?
5. How do we interpret the x-intercept from the equation?

**Tip:** Always try to verify a point on the graph to ensure accuracy in slope and intercept calculation.

What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.

Learn how to find the equation of a straight line by determining the slope and y-intercept from a graph. This problem includes algebraic concepts such as slope calculation and slope-intercept form. Suitable for students in Grades 8-10.

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