Question

PLS HELPPPPP!!!!!!!!!!!!!!!!!!!! 15 POINTS

The graph for the equation y = negative 2 x + 1 is shown below. On a coordinate plane, a line with negative slope goes through (0, 1) and (1, negative 1). If another equation is graphed so that the system has no solution, which equation could that be?
Options:
y = negative 2 (x minus one-half)
y = negative one-half (4 x + 2)
y = negative x + 1
y = negative one-half x + 2

Answer 1

b

Explanation:

i did test

Answer 2

y = negative 2 (x minus one-half)

Explanation:

The equation of a line is given as:

y = mx + c, where m is the slope and c is the intercept on the y axis.

The equation of a line going through (0, 1) and (1, - 1) is calculated using:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\ y-1=(-1-1)/(1-0)(x-0)\\ y-1=-2x\\y=-2x+1`

The solution of two lines is at their point of intersection. The equation of the line that would not have any solution with y = -2x + 1 would be a line that is parallel to y = -2x + 1. Since the two lines would be parallel to each other, their would be no intersection and therefore no solution.

Two lines are said to be parallel to each other if they have the same slope. The slope of y = -2x + 1 is gotten by comparing with y = mx + c, therefore the slope m = -2. From the options the only line with a slope m = -2 is y = -2(x -1/2). Therefore y = -2(x -1/2) is parallel to y = -2x + 1 and would have no solution