What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is \(\frac{2}{3}\)?
A
-2
B
-1
C
1
D
2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Gradient = \(\frac{y_2 - y_1}{x_2 - x_1}\)
\(\frac{2}{3}\) = \(\frac{4 - p}{p - (-1)}\)
\(\frac{2}{3}\) = \(\frac{4 - p}{p + 1}\)
3(4-p) = 2(p+1)
12 - 3p = 2p + 2
12 – 2 = 2p + 3p
10 = 5p
p= \(\frac{10}{5}\) = 2
Source: Myschool Past Questions Archive (Record #9334)