Question

A line in the xy-plane that passes through the coordinate points (3, -6) and (–7, –4) will never intersecta line that is represented by which of the following equations?

A, x+5y=6
B, x+(y/2)=7
C, y-2x=-9
D, 2y-x=-8

Answer 1

option A

Explanation:

given coordinate (3, -6) and (–7, –4)

to find the equation of line

slope of the line passing through both the point will be

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

`m = (-4+6)/(-7-3)`

`m = -(2)/(10)`

equation of line

( y - y₁ ) = m ( x - x₁ )

`y + 6= -(2)/(10)(x - 3)`

x + 5 y = -27

line which will not intersect will be parallel to it so option A has same slope as our line equation i.e. -1/5

hence, correct answer is option A