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To find the equation of the line in the form \( y = mx + c \), we need to determine the slope (\(m\)) and the y-intercept (\(c\)) of the line.

### Step 1: Determine the slope (\(m\))

The slope of the line is calculated using two known points on the line. Looking at the graph, we can extract two points:
- Point 1: \( (-60, -120) \)
- Point 2: \( (0, -40) \)

The formula for slope is:

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

Substitute the coordinates:

\[
m = \frac{-40 - (-120)}{0 - (-60)} = \frac{-40 + 120}{60} = \frac{80}{60} = \frac{4}{3}
\]

So, the slope \( m = \frac{4}{3} \).

### Step 2: Determine the y-intercept (\(c\))

The y-intercept (\(c\)) is where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at \( y = -40 \), so \( c = -40 \).

### Final equation of the line:

Now that we have \(m = \frac{4}{3}\) and \(c = -40\), the equation of the line is:

\[
y = \frac{4}{3}x - 40
\]

Would you like more details on any step or have any other questions?

Here are 5 related questions:
1. How can you find the slope of a line if only given the graph?
2. How does changing the slope (\(m\)) affect the appearance of a line?
3. What is the significance of the y-intercept in a linear equation?
4. How can you determine if two lines are parallel by looking at their equations?
5. What is the effect of changing the y-intercept (\(c\)) on the graph of a line?

**Tip:** The slope (\(m\)) tells us how steep the line is; a larger slope means a steeper line, while the sign of the slope indicates whether the line goes up or down as \(x\) increases.

Work out the equation of the 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 line from a graph. This problem involves determining the slope and y-intercept from the graph and applying the slope-intercept form of a linear equation (y = mx + c). Suitable for students in Grades 8-10.

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