The goal is to find the equation of the line shown on the graph in slope-intercept form, $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

Step 1: Find the y-intercept ($b$)

From the graph, the line crosses the y-axis at $y = 4$. So, the y-intercept is: $b = 4$

Step 2: Find the slope ($m$)

The slope is calculated using two points on the line. We can see that the line passes through:

• Point 1: $(-4, 6)$
• Point 2: $(0, 4)$

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(-4, 6)$ and $(0, 4)$: $m = \frac{4 - 6}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2}$

Step 3: Write the equation

Now that we have the slope and y-intercept, the equation of the line is: $y = -\frac{1}{2}x + 4$

Let me know if you'd like more details or have any questions!

Here are 5 related questions:

1. What is the general form of a linear equation?
2. How do you find the slope from two given points on a graph?
3. What does the slope of a line represent geometrically?
4. How can you identify the y-intercept directly from a graph?
5. How would the equation change if the slope were positive?

Tip: Remember, the slope can also be seen as the "rise over run," meaning how much the line goes up or down for every unit it moves horizontally.