https://file.aiquickdraw.com/mathbot/file/1727667524300vtj1pq86.jpg

The image you provided shows a straight line on a Cartesian coordinate plane. To analyze it, let's determine the equation of this line using the slope-intercept form, which is:

\[
y = mx + b
\]

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 \( m \)
The slope is the change in \( y \) over the change in \( x \) (also called "rise over run"). From the image, it appears that the line passes through the points \( (-10, 10) \) and \( (10, -10) \).

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

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

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

\[
m = \frac{-10 - 10}{10 - (-10)} = \frac{-20}{20} = -1
\]

### Step 2: Determine the y-intercept \( b \)
From the graph, the line crosses the y-axis at \( y = 0 \), so the y-intercept \( b = 0 \).

### Step 3: Write the equation
Now that we know the slope \( m = -1 \) and the y-intercept \( b = 0 \), the equation of the line is:

\[
y = -x
\]

This is the equation of the line shown in the graph.

Would you like any further details or explanations on this?

### 5 Related Questions:
1. How do you calculate the slope if the points are not given?
2. What is the significance of the y-intercept in a linear equation?
3. How can you find the x-intercept of a line from its equation?
4. What happens if the slope of a line is zero or undefined?
5. How can you graph a line given its slope and y-intercept?

### Tip:
When calculating the slope, remember that a negative slope means the line slopes downwards from left to right, while a positive slope means the line slopes upwards.

What is the equation of the line shown in the provided graph?

Learn how to find the equation of a line with a slope of -1 that passes through points (-10, 10) and (10, -10). This example uses the slope-intercept form of a linear equation and is suitable for students in Grades 8-10.

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