Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Points On Graph of Equation

Determine whether each point
lies on the graph of the equation.

Equation: y = sqrt{5 - x}

Points: A (1, 2), B (5, 0)

Let me see.

I basically have to evaluate the given function
at each x and y value. Yes? I must get the same result on both sides.

Point A

2 = sqrt{5 - 1}

2 = sqrt{4}

2 = 2

Point B

0 = sqrt{5 - 5}

0 = sqrt{0}

0 = 0

I say the points lie on the graph of the given equation but I don't fully understand why that is the case. After evaluating the given function at each point, I got the same answer on both sides. I know this could be the reason why the points lie on the graph of the equation but, if true, why is this correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,580

Re: Points On Graph of Equation

Yes, that's it exactly. An equation for a curve has the property that every pair of coordinates that fit the equation therefore lie on the curve and if the coordinates don't fit then that point isn't on the curve.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Points On Graph of Equation

Yes, that's it exactly. An equation for a curve has the property that every pair of coordinates that fit the equation therefore lie on the curve and if the coordinates don't fit then that point isn't on the curve.

Bob

After evaluating the equation at the given coordinates of the point at hand, the answer must be the same on both sides. This shows that the point lies on the graph of the equation.