Question

The equation LaTeX: Ax+By=10A x + B y = 10 goes through the coordinates (6, 5) and (-2, -5).

Answer 1

A=5 and B=-4.

Explanation:

The equation of line is

`Ax+By=10` .... (1)

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through the points (6, 5) and (-2, -5). So, the equation of line is

`y-5=(-5-5)/(-2-6)(x-6)`

`y-5=(-10)/(-8)(x-6)`

`y-5=(5)/(4)(x-6)`

Multiply both sides by 4.

`4(y-5)=5(x-6)`

`4y-20=5x-30`

`-20+30=5x-4y`

`10=5x-4y`

`5x-4y=10` .... (2)

On comparing (1) and (2) we get

`A=5,B=-4`

Therefore, A=5 and B=-4.