Question

A line passes through `(4 ,9 )` and `(2 ,5 )`. A second line passes through `(5 ,6 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(6 , 8)

Explanation:

The first step here is to calculate the gradient (m) of the line passing through the 2 given points using the `color(blue)" gradient formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( m = (y_2 - y_1)/(x_2 - x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 points "`

let `(x_1,y_1)=(4,9)" and " (x_2,y_2)=(2,5)`

`rArr m = (5-9)/(2-4) = (-4)/(-2) =2 =2/1`

Since the 2nd line is parallel then it's gradient will be = 2

There are an infinite number of points that lie on the 2nd line

However , using the definition of gradient we can get to the next point on the line from (5 , 6).

By moving 1 right and 2 up , equivalent to adding 1 to the x-coordinate and 2 to the y-coordinate.

hence (5 , 6 ) → (5+1 , 6+2) → (6 , 8)

Further points may be found in the same way.