To find the equation of the line from the graph, we need to determine two things:

1. The slope ($m$): This is the rate at which the line rises or falls. It is calculated as the ratio of the change in $y$ to the change in $x$ between two points on the line.
2. The y-intercept ($b$): This is the point where the line crosses the y-axis (when $x = 0$).

Step 1: Identify two points on the line.

From the graph, we can pick two points that the line passes through:

• $(-2, 0)$
• $(4, -3)$

Step 2: Calculate the slope.

The slope $m$ is given by the formula:

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

Using the points $(-2, 0)$ and $(4, -3)$: $m = \frac{{-3 - 0}}{{4 - (-2)}} = \frac{{-3}}{{4 + 2}} = \frac{{-3}}{{6}} = -\frac{1}{2}$

Step 3: Use the slope-intercept form.

The equation of a line in slope-intercept form is:

$y = mx + b$

We know $m = -\frac{1}{2}$. Now, to find $b$, we can use one of the points. Let's use $(-2, 0)$:

$0 = -\frac{1}{2}(-2) + b$ $0 = 1 + b \implies b = -1$

Final Equation:

Thus, the equation of the line is:

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

Would you like more details or have any questions about this? Here are some related questions for deeper understanding:

1. How do you calculate the slope from different pairs of points?
2. What is the significance of the y-intercept in a graph?
3. How would the equation change if the slope were positive?
4. Can you find the equation of a line using point-slope form?
5. How can the slope-intercept form be derived from the standard form of a line?

Tip: Always use clear points from the graph to ensure accuracy when calculating the slope and intercept.