The line \(3y + 6x\) = 48 passes through the points A(-2, k) and B(4, 8). Find the value of k.
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Correct Answer: Option B
Explanation:
The line: \(3y + 6x\) = 48
Divide through by 3
⇒ y + 2\(x\) = 16
⇒ y = -2\(x\) + 16
∴ The gradient of the line = -2
The points: A(-2, k) and B (4, 8)
m =\(\frac{y2 - y1}{x2 - x1} = \frac{8 - k}{4 - (-2)}\)
⇒ m =\(\frac[8 - k}{4 + 2} = {8 - k}{6}\)
Since the line passes through the points
∴ -2 = \(\frac{8 - k}{6}\)
⇒ \(\frac{-2}[1} = \frac{8 - k]{6}\)
⇒ 8 - k = -12
⇒ k = 8 + 12
∴ k = 20
The line: \(3y + 6x\) = 48
Divide through by 3
⇒ y + 2\(x\) = 16
⇒ y = -2\(x\) + 16
∴ The gradient of the line = -2
The points: A(-2, k) and B (4, 8)
m =\(\frac{y2 - y1}{x2 - x1} = \frac{8 - k}{4 - (-2)}\)
⇒ m =\(\frac[8 - k}{4 + 2} = {8 - k}{6}\)
Since the line passes through the points
∴ -2 = \(\frac{8 - k}{6}\)
⇒ \(\frac{-2}[1} = \frac{8 - k]{6}\)
⇒ 8 - k = -12
⇒ k = 8 + 12
∴ k = 20