The line $3y + 6x$ = 48 passes through the points A(-2, k) and B(4, 8). Find the value of k.

1. Analyze the question

We are given a linear equation $3y + 6x = 48$ and two points, $A(-2, k)$ and $B(4, 8)$, that lie on this line. We need to find the value of the unknown coordinate $k$ in point $A$.

2. Explain the concept

If a point lies on a line, its coordinates $(x, y)$ must satisfy the equation of that line. This means if we substitute the $x$ and $y$ values of the point into the equation, the left-hand side will equal the right-hand side. Since point $A(-2, k)$ is on the line $3y + 6x = 48$, we can substitute $x = -2$ and $y = k$ into the equation to solve for $k$.

3. Show the solution

Step 1: Write down the equation of the line. $3y + 6x = 48$

Step 2: Substitute the coordinates of point A(-2, k) into the equation. Here, $x = -2$ and $y = k$. $3(k) + 6(-2) = 48$

Step 3: Simplify the equation. $3k - 12 = 48$

Step 4: Solve for k. Add 12 to both sides of the equation: $3k = 48 + 12$ $3k = 60$

Divide both sides by 3: $k = \frac{60}{3}$ $k = 20$

(Self-check: We can verify this using point B(4, 8). If $x=4$ and $y=8$: $3(8) + 6(4) = 24 + 24 = 48$. This confirms the equation is correct.)

4. Identify the answer

Comparing our result $k = 20$ with the given options: A. 16 B. 20 C. 8 D. -2

The correct option is B.

5. Tip

When you are given a point $(x, y)$ and told it lies on a line, don't waste time calculating the slope unless necessary. Simply plug the $x$ and $y$ values directly into the equation and solve for the missing variable. It is a quick way to save time during your JAMB exam!