To determine the equation of the line shown on the graph, let's use the slope-intercept form of a line equation, which is:

$y = mx + b$

Where:

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

Step 1: Identify the y-intercept

From the graph, it is clear that the line crosses the y-axis at $-1$. Therefore, $b = -1$.

Step 2: Determine the slope (m)

The slope can be found by using two points on the line. Let's use the points:

• $(0, -1)$ (the y-intercept)
• $(2, -4)$

The formula for slope $m$ is:

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

Substitute the coordinates:

$m = \frac{-4 - (-1)}{2 - 0} = \frac{-4 + 1}{2} = \frac{-3}{2}$

So, the slope is $-\frac{3}{2}$.

Step 3: Write the equation

Now that we have the slope $m = -\frac{3}{2}$ and the y-intercept $b = -1$, the equation of the line is:

$y = -\frac{3}{2}x - 1$

Final Answer:

The correct equation is:

$y = -\frac{3}{2}x - 1$

This corresponds to the first option provided in the image.

Would you like further details or have any questions?

Related Questions:

1. How do you find the slope between two points?
2. What is the general form of a linear equation?
3. How do you graph a line given its equation?
4. What are the differences between slope-intercept and point-slope forms?
5. How do you determine the slope of vertical or horizontal lines?

Tip:

Always check for the y-intercept when writing the equation of a line; it helps identify the correct form quickly.