Answer:
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
The correct option is (1). [tex]y-x= -4[/tex]
Given equation,
[tex]y = x - 4[/tex]
the line, [tex]y = x - 4[/tex] passes through the points (0, -4) and (4, 0).
Comparing with the general equation of a straight line,
[tex]y = mx + c[/tex] , where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.
The slope of the equation [tex]y = x - 4[/tex] 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) [tex]y - x = -4[/tex]
[tex]y = x - 4[/tex]
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).
[tex]y - x = -2[/tex]
[tex]y=x-2[/tex]
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). [tex]y-x= -4[/tex]
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