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To determine the equation of the line shown on the graph, we follow the form \( y = mx + c \), where:

- \( m \) is the slope (gradient) of the line.
- \( c \) is the y-intercept (the point where the line crosses the y-axis).

### 1. Find the slope \( m \)
The slope \( m \) is calculated as:
\[
m = \frac{\text{rise}}{\text{run}}
\]
Looking at the graph:
- The line crosses two clear points: one at (0, 20) and another at (60, 140).
- The rise is \( 140 - 20 = 120 \).
- The run is \( 60 - 0 = 60 \).

Thus, the slope is:
\[
m = \frac{120}{60} = 2
\]

### 2. Find the y-intercept \( c \)
The y-intercept \( c \) is the value of \( y \) when \( x = 0 \). From the graph, the line crosses the y-axis at \( (0, 20) \), so \( c = 20 \).

### Final equation
Substituting \( m = 2 \) and \( c = 20 \) into the equation \( y = mx + c \):
\[
y = 2x + 20
\]

Let me know if you have any questions or would like more details!

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Here are 5 related questions to deepen your understanding:
1. How would you determine the equation if the line had a negative slope?
2. What does it mean for the slope to be 0? How would the graph look in that case?
3. How do you find the slope if the line doesn't pass through integer coordinates?
4. What is the equation of a vertical line passing through \( x = 5 \)?
5. How do parallel lines compare in terms of slope and y-intercept?

**Tip:** When calculating slope, make sure you choose points that are clear on the graph for accurate results!

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 determine the equation of a line from a graph in slope-intercept form (y = mx + c). This example uses two clear points from the graph to calculate the slope and the y-intercept, suitable for students in Grades 7-9.

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