To write the equation of the given line in slope-intercept form $y = mx + b$, we need to determine two key components: the slope ($m$) and the y-intercept ($b$).

Step 1: Identify two points on the line

From the graph:

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

Step 2: Calculate the slope ($m$)

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute $(-2, 4)$ and $(2, -4)$: $m = \frac{-4 - 4}{2 - (-2)} = \frac{-8}{4} = -2$ Thus, the slope is $m = -2$.

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

The y-intercept ($b$) is the value of $y$ when $x = 0$. Looking at the graph, the line crosses the y-axis at $y = 0$. Hence: $b = 0$

Step 4: Write the equation

Substitute $m = -2$ and $b = 0$ into the slope-intercept form $y = mx + b$: $y = -2x$

Final Answer:

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

Would you like additional explanations or help with verifying other points on the graph?

Here are five related questions for practice:

1. How do you find the equation of a line if only the slope and a single point are given?
2. Can you determine the equation of a vertical line? What would it look like?
3. What is the general method for converting a slope-intercept equation to standard form?
4. How does the graph change if you adjust the slope $m$ or y-intercept $b$?
5. Can you derive the equation of a line parallel to this one passing through a specific point?

Tip: When calculating slope, always double-check your subtraction order for $y_2 - y_1$ and $x_2 - x_1$ to avoid sign errors!