The graph for the equation y = x minus 4 is shown below. On a coordinate plane, a line goes through (0, negative 4) and (4, 0). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y minus x = negative 4 y minus x = negative 2

The correct option is (1).

Given equation,

the line, passes through the points (0, -4) and (4, 0).

Comparing with the general equation of a straight line,

, where is the slope and is the y-intercept.

The slope of the equation is 1 and its The y-intercept is -4.

We know that,

Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept.

Now we check for the slope and the intercept of the given options.

Option (1)  

Here the slope is 1 and y intercept is -4, which is the same as the given equation and both equations will have an infinite number of solutions.

Now option (2).

The slope is 1 and y intercept is -2  

The slope is the same as the given equation but the intercept is different giving no solution.

Hence the correct option is (1).

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The correct option is:

y - x = -4

Step-by-step explanation:

The graphed equation is:

y = x - 4

The equation which will have infinite number of solution should overlap the graphed equation at infinity points.

It is only possible when both the equations are exactly same.

Consider the line given:

y - x = -4

Rearrange the equation:

y = x - 4

Thus, it is the same as the first equation.

Verify for point (0,-4)

y - x = -4

-4 - 0 = -4

-4 = -4

Proved.

Verify for point (4,0)

y - x = -4

0 - 4 = -4

0 = -4+4

0 = 0

Proved

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.