Answer:
OPTION C: y = - |x - 2|
Step-by-step explanation:
To solve problems of this type take any two points on the graph. We take two points:
[tex]$ (x_1, y_1) = (2, 0) $[/tex] This means that when x = 2, y = 0.
And [tex]$ (x_2, y_2) = (0, -2) $[/tex]
These two points are on the given line.
So, these two points are substituted to check if they satisfy the given equation.
OPTION A: y = - |x + 2|
Substituting (2, 0):
LHS = y = 0
RHS = - |2 + 2| = - 4 ≠ 0
So, this option is eliminated.
OPTION B: y = - |x| + 2
Substitute (x, y) = (2, 0)
LHS = 0
RHS = - |2| + 2 = - 2 + 2 = 0
LHS = RHS
Now, check for (0, -2)
LHS = -2
RHS = - |0| + 2|
= - |0| + 2 = 2 ≠ -2
So, this option is eliminated as well.
OPTION C: y = - |x - 2|
Substitute (2, 0)
LHS = 0
RHS = - |2 - 2| = 0
LHS = RHS
Now, substitute (0, -2)
LHS = -2
RHS = - |0 - 2|
= - |- 2|
= - 2
∴ LHS = RHS for both the points.
OPTION D: y = - |x| - 2
Substitute (2, 0)
LHS = 0
RHS = - |2| - 2
= - 2 - 2
= - 4
This option is eliminated as well.
So, OPTION C is our answer since it satisfies the points.
NOTE: Points satisfying the equation of the graph is only a necessary condition not a sufficient one.
