What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is
2
3
?
Answer Details
The gradient of a line is the change in the y-coordinate divided by the change in the x-coordinate. So, for the line joining (-1,p) and (p,4), the gradient is (4-p)/(p-(-1)) or (4-p)/(p+1). We are given that this value is equal to 2/3.
So, we can set up the equation:
(4-p)/(p+1) = 2/3
To solve for p, we can cross-multiply and simplify:
3(4-p) = 2(p+1)
12-3p = 2p+2
10 = 5p
p = 2
Therefore, the value of p is 2.