Question

which of the following points lies on the line $y = x$?
a. $(-4, -4)$
b. $(-4, 4)$
c. $(4, -4)$
d. $(-4, 0)$

Explanation:

Step1: Recall the condition for a point \((x,y)\) to lie on the line \(y = x\)

A point \((x,y)\) lies on the line \(y=x\) if and only if the \(x\)-coordinate is equal to the \(y\)-coordinate, i.e., \(y=x\).

Step2: Check each option

• For option A: The point is \((-4,-4)\). Here, \(x = - 4\) and \(y=-4\). Since \(y=x\) (because \(-4=-4\)), this point satisfies the equation of the line \(y = x\).
• For option B: The point is \((-4,4)\). Here, \(x=-4\) and \(y = 4\). Since \(-4

eq4\), this point does not satisfy \(y=x\).

• For option C: The point is \((4,-4)\). Here, \(x = 4\) and \(y=-4\). Since \(4

eq - 4\), this point does not satisfy \(y=x\).

• For option D: The point is \((-4,0)\). Here, \(x=-4\) and \(y = 0\). Since \(-4

eq0\), this point does not satisfy \(y=x\).

Answer:

A. \((-4,-4)\)