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.