Question

How do I find five ordered pairs for \[y=2x+5\]?

Answer 1

Hint: Given a function \[y=f(x)\], we can find the ordered pairs for the function by substituting \[x=a\] in the equation of the function. By substituting \[x=a\] we get \[y=f(a)\], we should know that the \[\left( a,f(a) \right)\] is the coordinate of that lies on the graph of \[y=f(x)\].

Complete step by step answer:
We are given the function \[y=2x+5\], we are asked to find five ordered pairs for the given function. We know that we can find the ordered pairs for the function by substituting \[x=a\] in the equation of the function. Here, we have \[f(x)=2x+5\]. We need to find the five ordered pairs for a given expression, we will substitute five different values of x in the equation.
Substituting \[x=0\], we get \[y=2(0)+5=5\]. Hence, the first ordered pair is \[\left( 0,5 \right)\].
Substituting \[x=1\], we get \[y=2(1)+5=7\]. Hence the second ordered pair is \[\left( 1,7 \right)\].
Substituting \[x=2\], we get \[y=2(2)+5=4+5=9\]. Hence, the third ordered pair is \[\left( 2,9 \right)\].
Substituting \[x=3\], we get \[y=2(3)+5=6+5=11\]. Hence, the fourth ordered pair is \[\left( 3,11 \right)\].
Substituting \[x=4\], we get \[y=2(4)+5=8+5=13\]. Hence, the fourth ordered pair is \[\left( 4,13 \right)\].

The five ordered pairs are \[\left( 0,5 \right),\left( 1,7 \right),\left( 2,9 \right),\left( 3,11 \right),\left( 4,13 \right)\].

Note: We can find any number of ordered pairs for a given function by the same method. But we should be careful about one thing. We should not substitute values for which the function becomes undefined or values that are not part of the domain of function.
For example, for the function, \[\sqrt{x}\] we cannot substitute negative values as they are not in the domain of function. Also, for the function, \[\dfrac{1}{x}\] we cannot substitute \[x=0\] as the function becomes undefined for this value.