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

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Re: For what ordered pair (x, y) on the graph of y = 1/2*x - 1 [#permalink]
Bunuel wrote:
For what ordered pair (x, y) on the graph of $$y=\frac{1}{2}x-1$$ does the x-coordinate equal the y-coordinate?

A. (-2,-2)

B. (1/2,1/2)

C. (1,-1/2)

D. (2,1)

E. (2,2)

Solution:

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

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.
Re: For what ordered pair (x, y) on the graph of y = 1/2*x - 1 [#permalink]
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