To write the equation of the line shown in the image in slope-intercept form, we need two pieces of information:

1. The slope of the line.
2. The y-intercept (the point where the line crosses the y-axis).

Step 1: Identify two points on the line

Looking at the graph, the line passes through two clear points:

• Point 1: $(-10, 5)$
• Point 2: $(10, -1)$

Step 2: Calculate the slope

The slope $m$ is calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of the two points: $m = \frac{-1 - 5}{10 - (-10)} = \frac{-6}{20} = -\frac{3}{10}$

Step 3: Determine the y-intercept

To find the y-intercept $b$, we use the slope-intercept form of the line equation:

$y = mx + b$

Substitute the slope $m = -\frac{3}{10}$ and one of the points, say $(10, -1)$, into the equation: $-1 = -\frac{3}{10}(10) + b$

Simplifying: $-1 = -3 + b \implies b = -1 + 3 = 2$

Step 4: Write the equation

Now that we have the slope $m = -\frac{3}{10}$ and the y-intercept $b = 2$, the equation of the line is:

$y = -\frac{3}{10}x + 2$

This is the equation in slope-intercept form.

Would you like any further details or explanations?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the slope if you have two points?
2. What does the y-intercept represent in a linear equation?
3. How would the equation change if the slope was positive?
4. Can you find the equation of a line if the y-intercept is not given but two points are?
5. How would you write the equation if it were in point-slope form instead?

Tip: When calculating the slope, always subtract the coordinates in the same order (i.e., always $y_2 - y_1$ and $x_2 - x_1$) to avoid sign errors.