Question

The graph for the equation y = negative x + 2 is shown below.
On a coordinate plane, a line with positive slope goes through (0, 2) and (2, 0).
If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
y = negative 2 (x minus 1)
y = negative (x + 2)
y = negative one-fourth (4 x minus 8)
y = negative one-half (x + 4). i will mark brianliest if our get it right PLZ

Answer 1

Answer:

I don't know answer but please mark me as brainlist

Answer 2

c) y = negative one-fourth (4 x minus 8) is the solution.

Given,

Equation y = -x +2

To find,

Another line such that they have infinite solutions.

Solution,

A pair of lines have infinite solutions when they are parallel and overlap with each other.

To check if the lines are parallel, we can look at the slope of the lines and tell. But for the lines to be overlapping, the other condition is meant to be fullfilled. Its intercept should also be the same.

Mathematically we can say that any equation of the form,

y = λ( -x +2 ) where λ belongs to a rational number parallel to the given line.

Considering the third option and representing it in the form of the equation we have,

y = -1/4( 4x -8 )

y = 1/4 * 4 ( -x + 2 )

In the given equation, the value of λ comes out to be 1/4*4 = 1.

Therefore, the lines y = negative one-half (x + 4) and y = -x + 2 will have infinitely many solutions.