Question

The gradient of the line passing through A (2,3), B (k,7) is

23
23

. Find the value of k. help pls

Answer 1

Given:

The gradient of the line passing through A(2,3), B(k,7) is
`(2)/(3)`.

To find:

The value of k.

Solution:

The gradient or slope of a line is:

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

The gradient of the line passing through A(2,3), B(k,7) is
`(2)/(3)`. So,

`(2)/(3)=(7-3)/(k-2)`

`(2)/(3)=(4)/(k-2)`

On cross multiplication, we get

`2(k-2)=4(3)`

`2k-4=12`

`2k=12+4`

`2k=16`

Divide both sides by 2.

`k=(16)/(2)`

`k=8`

Therefore, the value of k is 8.