For what ordered pair (x, y) on the graph of y = 1/2*x - 1

Solution:

Since the question tells us "x-coordinate equal the y-coordinate". we can easily eliminate options C and D.

There are a couple of ways to go about this problem.


Method 1:

We can plug in the values in the options and see which one is satisfying the equation.

Option A: (-2,-2)

We can plug \(x=y=-2\) in the equation \(y=\frac{1}{2}x-1 \).

\(⇒ -2=\frac{1}{2}\times -2-1\)

\(⇒ -2=-1-1\)
.
\(⇒-2=-2\)

We see that \(x=y=-2\) is satisfying the equation and thus will be the answer. Similarly we can check other options as well.


Method 2:

We can just \(x=y\) in the equation and get the value of \(x\).

We have: \(y=\frac{1}{2}x-1 \)

\(⇒ x=\frac{1}{2}x-1\)

\(⇒ x=\frac{x}{2}-1\)

\(⇒ x-\frac{x}{2}=-1\)

\(⇒ \frac{2x-x}{2}=-1\)

\(⇒ x=-2\)

Thus, we get \(x=y=-2\).

Hence the right answer is Option A.