What is the ordered pair?

Question

What are the three the ordered pairs of: X/2-3y=5

Is the equation linear? Yes/no?

(4,_) (_,2) (10,_)

Answer 1

You want to begin by rewriting the equation in y = mx + b form.

x/2 - 3y = 5 (Let's move x/2 to the other side by subtracting it from both sides)

-x/2 -x/2

-3y = -x/2 +5 (Now we want it to just be y not -3y so we divide both sides by -3)

y = x/6 - 5/3

We have rewritten the equation as y = x/6 - 5/3 or y = 1/6x - 5/3 so the slope is 1/6 and the y-intercept is -5/3. Since we were able to rewrite it in y = mx+b form, it is a linear equation.

Next, we want to solve for the ordered pairs. In an ordered pair, the first number is an x-value and the second number is a y-value (x,y). You are given the ordered pairs (4,_) (_,2) (10,_) so for the first ordered pair the x-value is 4. We need to solve for the y-value. We go back to our equation and plug in our x-value.

y = x/6 - 5/3

y = 4/6 - 5/3 (we need the same denominator to subtract fractions so we need the least common multiple, which is 6 in this case)

y = 4/6 - 10/6

y = -6/6 = -1

Thus, the ordered pair is (4,-1).

The great thing about algebra is we can check our work ourselves by plugging in, like shown:

We can plug into either the original equation or the same equation rewritten in y=mx+b). Let's try the original:

X/2 - 3y = 5

4/2 - 3(-1) = 5

2 + 3 = 5

5 = 5 (it worked!)

We do these same steps for the other two ordered pairs. For the ordered pair (_,2), 2 is the y-value.

y = x/6 - 5/3

2 = x/6 - 5/3 (We need to isolate x so let's add 5/3 on both sides)

2 + 5/3 = x/6

6/3 + 5/3 = x/6

11/3 = x/6 (Now, we need to multiply by 6 on both sides to solve for x)

x = 22 so the ordered pair is (22,2).

Let's check our work:

X/2 - 3y = 5

22/2 - 3(2) = 5

11 - 6 = 5

5 = 5 (it worked!)

For the last ordered pair, we have (10,_). The x-value is 10 so we plug that in.

y = x/6 - 5/3

y = 10/6 - 5/3 (we need the same denominator to subtract fractions so we need the least common multiple, which is 6 in this case)

y = 10/6 - 10/6

y = 0

Thus, the ordered pair is (10,0).

Let's check our work once more:

X/2 - 3y = 5

10/2 - 3(0) = 5

5 - 0 = 5

5 = 5 (it worked!)

I hope this helped! Please let me know if I can clarify anything or if you would like individual Algebra tutoring. I'd be happy to help. :)