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To determine the equation of the straight line in the form \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept, let's proceed with the following steps:

### 1. Identify two points on the line
From the graph, we can choose two clear points that lie on the line:
- The line crosses the y-axis at the point \( (0, 6) \). This means the y-intercept \( c = 6 \).
- Another point on the line is \( (2, 0) \) because the line crosses the x-axis there.

### 2. Calculate the slope \( m \)
The slope \( m \) of a line is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 6) \) and \( (2, 0) \):
\[
m = \frac{0 - 6}{2 - 0} = \frac{-6}{2} = -3
\]
Thus, the slope of the line is \( m = -3 \).

### 3. Write the equation of the line
Now that we know the slope \( m = -3 \) and the y-intercept \( c = 6 \), the equation of the line is:
\[
y = -3x + 6
\]

This is the equation of the line in the required form.

Would you like more details or further clarifications?

### Related questions:
1. How can you derive the equation of a line from just the slope and one point?
2. What is the significance of the y-intercept in the equation of a line?
3. How do you calculate the slope if only one point and the equation are given?
4. Can you describe a method to find the equation if the line doesn't cross the axes clearly?
5. How does changing the slope affect the appearance of the line?

### Tip:
Always check two distinct points on the graph to accurately calculate the slope when determining the equation of a line.

Work out 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.

Explore how to determine the equation of a straight line by identifying points and calculating the slope. This tutorial covers the slope formula and the equation y = mx + c, ideal for students in Grades 8-10.

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