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
`-(1)/(2)`.

To find:

The value of p.

Solution:

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

`m=(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=(p-5)/(2-(-2))`

`m=(p-5)/(2+2)`

`m=(p-5)/(4)`

It is given that the gradient or slope of the line is
`-(1)/(2)`.

`(p-5)/(4)=-(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.