We are asked to find the equation of the straight line $y = k \cdot x + q$, which passes through the points $A(-1, 3)$ and $B(2, 6)$. To do this, we need to find the values of $k$ (the slope) and $q$ (the y-intercept).

Step 1: Calculate the slope $k$

The slope $k$ of the line passing through two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by: $k = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of $A(-1, 3)$ and $B(2, 6)$: $k = \frac{6 - 3}{2 - (-1)} = \frac{3}{3} = 1$

Step 2: Find the y-intercept $q$

Now that we know the slope $k = 1$, we can use the equation of the line $y = k \cdot x + q$ to find $q$. We can substitute the coordinates of one of the points, say point $A(-1, 3)$, into the equation.

Using $A(-1, 3)$: $3 = 1 \cdot (-1) + q$ $3 = -1 + q$ $q = 4$

Final Equation of the Line:

The equation of the line is: $y = 1 \cdot x + 4 \quad \text{or simply} \quad y = x + 4$

So, $k = 1$ and $q = 4$.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. How do you derive the equation of a line from different forms (e.g., point-slope)?
2. What is the geometric significance of the slope $k$?
3. How can you calculate the distance between two points in a plane?
4. What happens to the line equation if one of the points is on the y-axis?
5. How can the midpoint formula help when finding the center between two points?

Tip: Always verify the slope calculation before substituting into the line equation to avoid sign errors.