Let's analyze and solve the problem step by step.

Step 1: Identify the equation of the line

The general form of the equation of a line is: $y = mx + b$ where $m$ is the slope, and $b$ is the y-intercept.

Step 2: Calculate the slope ($m$)

The slope is calculated using two points on the line: $m = \frac{y_2 - y_1}{x_2 - x_1}$ The points provided are $(-2, -3)$ and $(2, 3)$. Plugging in these coordinates: $m = \frac{3 - (-3)}{2 - (-2)} = \frac{3 + 3}{2 + 2} = \frac{6}{4} = \frac{3}{2}$

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

Using the slope $m = \frac{3}{2}$, substitute one of the points into the equation $y = mx + b$. We'll use the point $(2, 3)$: $3 = \frac{3}{2}(2) + b$ $3 = 3 + b$ $b = 3 - 3 = 0$

Step 4: Write the equation

The equation of the line is: $y = \frac{3}{2}x + 0$ or simply: $y = \frac{3}{2}x$

Would you like further explanation or have additional questions?

Related Questions:

1. How do you determine the slope when the points are fractions?
2. What if the line is vertical or horizontal—how would the equation change?
3. How do you verify the equation of a line using substitution?
4. Can the equation of a line always be simplified to slope-intercept form?
5. What happens if there is a third point on the line—how would it affect the equation?

Tip:

When calculating the slope, always simplify the fraction completely to avoid errors in the final equation.