Let's start by finding the equation of the line that passes through the first and last data points, which are $(-2, -4)$ and $(2, 5)$.

Step 1: Find the slope of the line

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For the points $(-2, -4)$ and $(2, 5)$: $m = \frac{5 - (-4)}{2 - (-2)} = \frac{5 + 4}{2 + 2} = \frac{9}{4}$

Step 2: Use the point-slope form to find the equation

Now that we have the slope, we can use the point-slope form of a line equation, which is:

$y - y_1 = m(x - x_1)$

Using the point $(-2, -4)$ and $m = \frac{9}{4}$:

$y - (-4) = \frac{9}{4}(x - (-2))$ $y + 4 = \frac{9}{4}(x + 2)$

Step 3: Simplify the equation

Distribute the slope:

$y + 4 = \frac{9}{4}x + \frac{9}{4} \times 2$ $y + 4 = \frac{9}{4}x + \frac{18}{4}$ $y + 4 = \frac{9}{4}x + \frac{9}{2}$

Now subtract 4 from both sides to isolate $y$:

$y = \frac{9}{4}x + \frac{9}{2} - 4$ $y = \frac{9}{4}x + \frac{9}{2} - \frac{8}{2}$ $y = \frac{9}{4}x + \frac{1}{2}$

Final Answer:

The equation of the line passing through the first and last points is:

$y = \frac{9}{4}x + \frac{1}{2}$

Would you like details on how to graph this, or any further clarification? Here are 5 related questions for practice:

1. How would you find the equation of a line if given two different points?
2. What is the slope-intercept form of a line, and how does it differ from the point-slope form?
3. How do you interpret the slope in a real-world scenario?
4. What are the steps to plot a line given its equation?
5. How can you verify that a point lies on a given line?

Tip: Always check if your calculated slope makes sense visually by comparing it to the steepness of the line on a scatter plot!