Question

If point A, havingcoordinates (p, 3) andpoint B, with coordinates(6, p) lie on a line havinga slope of 2, what is thevalue of p?

Answer 1

Take into account that the slope of a line is given by the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

where (x1,y1) and (x2,y2) are two points on the line.

In this case:

(x1,y1) = (p,3)

(x2,y2) = (6,p)

By replacing the previous values into the formula for m, we get:

`m=(p-3)/(6-p)`

Now, by making m = 2 and solving for p, we obtain:

`\begin{gathered} (p-3)/(6-p)=2 \\ p-3=2(6-p) \\ p-3=12-2p \\ p+2p=12+3 \\ 3p=15 \\ p=(15)/(3)=5 \end{gathered}`

Hence, the value of p is p = 5