To find the equation of the line represented in the graph, we use the slope-intercept form of a line:

$y = mx + b$ where:

• $m$ is the slope of the line.
• $b$ is the $y$-intercept (the point where the line crosses the $y$-axis).

Step 1: Find the slope ($m$)

The slope is given by:

$m = \frac{\text{rise}}{\text{run}}$

From the graph:

• The line passes through the points $(-8, 6)$ and $(0, -2)$.
• Calculate the slope between these two points:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 6}{0 - (-8)} = \frac{-8}{8} = -1$

Thus, the slope $m = -1$.

Step 2: Find the $y$-intercept ($b$)

The $y$-intercept is the point where $x = 0$. From the graph, we observe that:

$b = -2$

Step 3: Write the equation

Substitute the values of $m$ and $b$ into the slope-intercept form:

$y = -x - 2$

Final Answer:

$y = -x - 2$

Would you like me to verify this equation or explain any part in more detail?

Related Questions:

1. How do you calculate the slope if you are given two points?
2. What is the general form of a linear equation, and how is it different from slope-intercept form?
3. How can you identify the slope and $y$-intercept directly from a graph?
4. How do you convert the slope-intercept form into standard form?
5. Can you explain how the slope relates to the steepness of the line?

Tip: Always double-check that the line passes through known points after calculating the equation.