Question

The graphed line shown below is y=-4x-12. Which equation, when graphed with the given equation, will form a system that has no solution?

Answer 1

`y=-4x`

Explanation:

A Linear System with no solution, therefore inconsistent, is graphically represented by a pair of parallel lines.

According to Analytic Geometry, a parallel line shares the same slope.

Given the options, the only parallel line to
`y=-4x-12` is
`y=-4x` Since
`y=-4(x+3)` despite having the same slope, is actually the same line
`y=-4x+12`

So
`y=-4x` will form a system that has no solution.

Answer 2

I guess one more does not hurt.

Notice that choice D is equivalent to the given equation y = -4x - 12.

The only equation that does not cross the given equation is y = -4x.

They have THE SAME SLOPE. This means they are parallel and thus lead to NO SOLUTION.

ANSWER: y = -4x