To write the equation of the line from the graph, we need to determine two things: the slope (m) and the y-intercept (b).

Step 1: Identify the slope (m)

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run). We can pick two points from the graph to calculate this. Based on the image, two clear points are:

• Point 1: (0, 2) (y-intercept)
• Point 2: (-2, 0) (x-intercept)

Using the formula for slope: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{0 - 2}}{{-2 - 0}} = \frac{{-2}}{{-2}} = 1$

So, the slope of the line is 1.

Step 2: Identify the y-intercept (b)

From the graph, the line crosses the y-axis at y = 2. Therefore, the y-intercept is 2.

Step 3: Write the equation

The equation of a line is given by the slope-intercept form: $y = mx + b$ Substituting the values we found for the slope $m = 1$ and y-intercept $b = 2$, the equation becomes: $y = x + 2$

Final Answer:

The equation of the line is: $y = x + 2$

Do you need more details or have any questions?

Here are 5 related questions to expand on this concept:

1. How do you find the slope of a line if the two points aren't as clearly defined?
2. What happens to the slope when the line is horizontal or vertical?
3. How do you convert an equation from standard form (Ax + By = C) to slope-intercept form?
4. Can you derive the equation if you're only given the slope and one point on the line?
5. How does the equation change if the slope is negative?

Tip: The slope indicates how steep a line is. A positive slope means the line rises from left to right, while a negative slope means it falls.