The problem asks for the equation of the line shown on the graph.

From the image:

1. Identifying two points: Let's pick two points that the line passes through. Looking at the graph:

   • Point 1: $(-5, 2)$
   • Point 2: $(3, -2)$

2. Find the slope ($m$): The slope of a line is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values of the two points: $m = \frac{-2 - 2}{3 - (-5)} = \frac{-4}{8} = -\frac{1}{2}$ So, the slope $m = -\frac{1}{2}$.

3. Find the equation using the point-slope form: The equation of a line in point-slope form is: $y - y_1 = m(x - x_1)$ Using one of the points, say $(-5, 2)$, and the slope $m = -\frac{1}{2}$, the equation becomes: $y - 2 = -\frac{1}{2}(x + 5)$ Simplifying: $y - 2 = -\frac{1}{2}x - \frac{5}{2}$ $y = -\frac{1}{2}x - \frac{5}{2} + 2$ $y = -\frac{1}{2}x - \frac{1}{2}$

Thus, the equation of the line is: $y = -\frac{1}{2}x - \frac{1}{2}$

Would you like further details on any step, or do you have any questions?

Here are 5 related questions to practice:

1. What would the equation be if the slope was positive?
2. How do you calculate the y-intercept directly from the equation?
3. Can you rewrite the equation in standard form?
4. What is the slope-intercept form of a line, and how does it relate to this equation?
5. How do you find the equation of a line if you only have its slope and y-intercept?

Tip: Always double-check the points chosen from a graph for accuracy when calculating the slope!