To find the equation of the line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, let's break down the components from the image:

1. Slope (m):

The slope of the line can be calculated using the formula: $m = \frac{\text{rise}}{\text{run}}$ From the image, the line passes through two points: (-4, 0) and (0, -2).

• Rise: The vertical change between the two points is from $y = 0$ to $y = -2$, giving a rise of -2.
• Run: The horizontal change between the two points is from $x = -4$ to $x = 0$, giving a run of 4.

Thus, the slope $m = \frac{-2}{4} = -\frac{1}{2}$.

2. Y-intercept (b):

The y-intercept $b$ is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $y = -2$, so $b = -2$.

Final Equation:

Substituting $m = -\frac{1}{2}$ and $b = -2$ into the slope-intercept form: $y = -\frac{1}{2}x - 2$

Would you like more details on how to find the slope or intercept?

Here are five related questions:

1. How do you calculate the slope if given two points?
2. What does the y-intercept represent in the equation of a line?
3. Can the slope of a line ever be zero or undefined?
4. How does the slope affect the direction and steepness of a line?
5. How can you find the equation of a line if given a point and the slope?

Tip: When identifying the slope on a graph, always check the vertical (rise) and horizontal (run) distances carefully to ensure correct sign and value!