Question

The line passing through (-2,5) and (2,p) has a gradient of -1/2.

Fnd the value of p

Answer 1

Given:

The line passing through (-2,5) and (2,p) has a gradient of $-\dfrac{1}{2}$.

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

The line passing through (-2,5) and (2,p). So, the slope of the line is:

$m=\dfrac{p-5}{2-(-2)}$

$m=\dfrac{p-5}{2+2}$

$m=\dfrac{p-5}{4}$

It is given that the gradient or slope of the line is $-\dfrac{1}{2}$.

$\dfrac{p-5}{4}=-\dfrac{1}{2}$

On cross multiplication, we get

$2(p-5)=-4(1)$

$2p-10=-4$

$2p=-4+10$

$2p=6$

Divide both sides by 2.

$p=3$

Therefore, the value of p is 3.