To determine the equation of the line in slope-intercept form ($y = mx + b$) from the graph:

Step 1: Identify the slope ($m$)

The slope is the "rise over run." From the graph:

• Pick two points on the line. From observation, the points $(0, -2)$ and $(2, 0)$ are on the line.
• The slope $m = \frac{\text{rise}}{\text{run}} = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1$.

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

The y-intercept is the point where the line crosses the $y$-axis. From the graph, this is $(0, -2)$. Therefore, $b = -2$.

Step 3: Write the equation

Substitute $m = 1$ and $b = -2$ into the slope-intercept form equation: $y = mx + b$ $y = x - 2$

Final Answer:

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

Would you like additional details or further explanations?

Related Questions:

1. How can the slope be calculated if the points are not obvious?
2. What are the properties of a line with a slope of 1?
3. How does changing the y-intercept affect the graph of a line?
4. What is the equation of a line parallel to this one passing through a different point?
5. How can this line's equation be converted into standard form?

Tip: Always double-check your chosen points when