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Write the equation of the line in fully simplified form

To find the equation of the line shown in the image, we can use the slope-intercept form of a line equation:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

### Step 1: Determine the slope \( m \)
To calculate the slope, we need two points on the line. From the graph, we can pick two points where the line crosses the grid neatly:
- Point 1: \( (-10, 10) \)
- Point 2: \( (0, 5) \)

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Substitute the points \( (-10, 10) \) and \( (0, 5) \):

\[
m = \frac{5 - 10}{0 - (-10)} = \frac{-5}{10} = -\frac{1}{2}
\]

### Step 2: Determine the y-intercept \( b \)
From the graph, the line crosses the y-axis at \( y = 5 \), so the y-intercept \( b = 5 \).

### Step 3: Write the equation
Now that we have the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 5 \), we can write the equation of the line:

\[
y = -\frac{1}{2}x + 5
\]

This is the fully simplified equation of the line.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you find the slope if the line is vertical?
2. What is the meaning of a positive versus negative slope?
3. How can you rewrite the equation of the line in point-slope form?
4. How would the equation change if the line were steeper?
5. What if the line passed through the origin—how would the equation be affected?

**Tip:** Always make sure to use points that lie exactly on the grid intersections when calculating slope from a graph for greater accuracy.

Write the equation of the line in fully simplified form.

Discover how to find the equation of a line using slope-intercept form with a detailed step-by-step solution. Learn to identify the slope and y-intercept from a graph to write the fully simplified equation y = -1/2x + 5. Ideal for students in Grades 8 to 10.

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