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

Step 1: Identify two points on the line

From the image, two clear points on the line are:

• Point 1: $(0, -2)$
• Point 2: $(4, 2)$

Step 2: Calculate the slope ($m$)

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of the two points: $m = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1$

So, the slope ($m$) is $1$.

Step 3: Determine the y-intercept ($b$)

The y-intercept is where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $b = -2$.

Step 4: Write the equation

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

Final Answer:

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

Let me know if you want further clarification or have additional questions.

Related Questions:

1. How can you determine the slope of a line from a graph?
2. What is the significance of the y-intercept in the equation of a line?
3. How do you rewrite the equation in standard form ($Ax + By = C$)?
4. What does a slope of 1 mean in real-world contexts?
5. How would the equation change if the line were shifted vertically?

Tip: Always check your slope calculation by verifying with additional points along the line.