To find the equation of the line from the graph, we need to use the slope-intercept form of a line equation:

$y = mx + b$

Where:

• $m$ is the slope of the line
• $b$ is the y-intercept (the value of $y$ when $x = 0$)

1. Finding the slope (m):

To find the slope, we can use two points on the line. From the graph:

• One point is approximately $(-4, -2)$
• Another point is $(0, 2)$ (the y-intercept)

The slope $m$ is given by the formula:

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

Substitute the values of the two points $(-4, -2)$ and $(0, 2)$:

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

So, the slope $m = 1$.

2. Finding the y-intercept (b):

From the graph, we can see that the line crosses the y-axis at $y = 2$, so the y-intercept $b = 2$.

Final Equation:

Substituting $m = 1$ and $b = 2$ into the equation $y = mx + b$:

$y = x + 2$

This is the equation of the line.

Would you like further details on the steps? Here are some additional related questions to explore:

1. How do we find the equation if we only know one point and the slope?
2. What is the general form of the equation of a line?
3. How do we determine the slope of a vertical or horizontal line?
4. Can the slope of a line ever be negative, and how would that affect the equation?
5. How would you find the equation of a line parallel or perpendicular to this one?

Tip: Always check the values of the points you choose to calculate the slope to avoid errors in the equation.