https://file.aiquickdraw.com/mathbot/file/1728470925412m6z5bgoj.jpg

Let's analyze the graph to find the equation of the straight line.

We need to express the equation in the form \( y = mx + c \), where:
- \( m \) is the slope of the line (rise over run).
- \( c \) is the y-intercept (the point where the line crosses the y-axis).

### Step 1: Identify two points on the line
From the graph, we can see that the line passes through the following points:
- \( (-6, 0) \) (x-intercept)
- \( (0, 6) \) (y-intercept)

### Step 2: Calculate the slope (\( m \))
The slope is given by:
\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (-6, 0) \) and \( (0, 6) \):
\[
m = \frac{6 - 0}{0 - (-6)} = \frac{6}{6} = 1
\]
So, the slope \( m = 1 \).

### Step 3: Identify the y-intercept (\( c \))
From the graph, it's clear that the y-intercept \( c \) is 6 (the point where the line crosses the y-axis).

### Final Equation:
The equation of the line is:
\[
y = 1x + 6 \quad \text{or simply} \quad y = x + 6
\]

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

### Further Related Questions:
1. How do you find the equation of a line if you only know the slope and one point?
2. What happens to the equation of a line when the slope is negative?
3. How can we determine the slope if the points are fractions or decimals?
4. What is the general form of a straight line equation?
5. How does the y-intercept affect the position of the line on the graph?

**Tip:** When calculating the slope, remember that it represents how steep a line is, with positive slopes going up and negative slopes going down.

What is the equation of the straight line shown in the graph? Provide your answer in the form y = mx + c.

Learn how to find the equation of a straight line from a graph using the slope and y-intercept. This problem covers key algebraic concepts and provides a step-by-step solution, suitable for students in Grades 8-10.

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