To find the equation of the line, we use the slope-intercept form of a linear equation:

$f(x) = mx + b$

Here:

• $m$ is the slope of the line,
• $b$ is the $y$-intercept.

Step 1: Find the slope $m$

To calculate the slope, use the formula:

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

From the graph:

• One point on the line is $(-1, 0)$ (the $y$-intercept).
• Another point is $(0, -2)$.

Substitute into the slope formula:

$m = \frac{-2 - 0}{0 - (-1)} = \frac{-2}{1} = -2$

So, the slope $m$ is $-2$.

Step 2: Identify the $y$-intercept $b$

From the graph, the line crosses the $y$-axis at $b = -2$.

Step 3: Write the equation

Substitute $m = -2$ and $b = -2$ into the slope-intercept form:

$f(x) = -2x - 2$

Final Answer:

The equation of the line is:

$f(x) = -2x - 2$

Would you like a step-by-step explanation of how to calculate the slope or intercept in detail?

Here are some related questions to practice:

1. How do you determine the slope if the two points are given explicitly?
2. How can you write a line's equation if the slope and a point are given?
3. What is the general formula for a line passing through two given points?
4. How does changing the slope $m$ affect the line's graph?
5. How do you find the equation of a vertical or horizontal line?

Tip: Remember, the slope $m$ tells you how steep the line is. A negative slope makes the line slant downwards from left to right.