Find the gradient of lines joining the following pair of points.

Question

If, $Gradient = \frac{(y_2-y_1)}{(x_2-x_1)}$

And, $(x_1,y_1),(x_2,y_2) = (p+3, p-3), (3p+4, p-5)$

Then, $(y_2,y_1) = ((p-5)-(p-3))$

$=((p-5)-p+3)$

$=(p-5-p+3)$

$=(-2)$

And, $(x_2,x_1) = ((3p+4)-(p+3))$

$=((3p+4)-p-3)$

$=(3p+4-p-3)$

$=(2p+1)$

So,

$Gradient = \frac{(-2)}{(2p+1)}$

$Gradient = -0.5p-1$

The textbook says $-2$, where have I gone wrong?

Answer 1

Just so this question gets answered (and if you are satisfied then consider accepting):

The slope (or gradient) of the line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is as you say equal to $(y_2-y_1)/(x_2-x_1)$. Thus in this case we find \begin{align} \text{Gradient}&=\frac{(p-5)-(p-3)}{(3p+4)-(p+3)} \\ &=\frac{-2}{2p+1}. \end{align} As I mentioned in the comment, this only equals $-2$ when $p=0$.