The task is to write the equation of the given line in slope-intercept form, $y = mx + b$.

1. Finding the slope ($m$): To find the slope, identify two points on the line:

   • Point 1: (-8, 5)
   • Point 2: (0, -3)

   The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates: $m = \frac{-3 - 5}{0 - (-8)} = \frac{-8}{8} = -1$

   The slope ($m$) is $-1$.

2. Finding the y-intercept ($b$): The y-intercept ($b$) is the value of $y$ when $x = 0$. From Point 2, we know: $b = -3$

3. Writing the equation: Substitute $m = -1$ and $b = -3$ into the slope-intercept form: $y = -x - 3$

Final Equation:

$y = -x - 3$

Let me know if you would like further clarification or details! Here are some related questions for practice:

1. How do you verify a point lies on a given line?
2. What is the significance of the slope in a line equation?
3. How would the equation change if the slope were positive?
4. How can you rewrite the equation in standard form $Ax + By = C$?
5. What happens to the graph if you change the $b$-value while keeping the slope constant?

Tip: Always verify your slope and y-intercept by substituting points from the graph into your equation.