For the table to the​ right, represent the relationship using​ words, an​ equation, and a graph. Then determine whether the relationship is a linear function.

Question

x

y

0
5
1
7
2
9
3
11
Question content area bottom
Part 1
Represent the relationship using words. Choose the correct answer below.
A.
The value of y is five

more

than the quantity two

times the value of x.
Your answer is correct.
B.
The value of y is six

less

than the quantity two

times the value of x.
C.
The value of y is the cube

of the quantity two

plus

the value of x.
D.
The value of y is two

less

than the square

of the quantity seven

times the value of x.
E.
The value of y is six

times the value of x.
F.
The value of y is the square

of the quantity four

minus

the value of x.
Part 2
Represent the relationship using an equation.
yequals
11
​(Simplify your answer. Type an expression using x as the​ variable.)

Answer 1

Part 1:
To represent the relationship using words, we need to look at how the value of y changes with respect to x.

From the given table:
- When x = 0, y = 5
- When x = 1, y = 7
- When x = 2, y = 9
- When x = 3, y = 11

We can observe that as x increases by 1, y increases by 2. Therefore, the relationship between x and y is that y is 2 times x plus a constant value.

The correct statement that represents this relationship is:
A. The value of y is five more than the quantity two times the value of x.

This reflects the pattern seen in the table, where y = 2 * x + 5.

Part 2:
To represent the relationship using an equation, we use the pattern identified in Part 1. Since y is always 5 more than 2 times x, the equation is:

y = 2x + 5

Graph:
To graph the relationship, plot the given points (0,5), (1,7), (2,9), and (3,11) on a coordinate plane, and then draw a straight line through these points since they are collinear. This line is the graphical representation of the equation y = 2x + 5.

In conclusion, the relationship is indeed a linear function because the equation is of the form y = mx + b, where m and b are constants. In this case, m (the slope) is 2, and b (the y-intercept) is 5. This linear function describes a straight line when graphed on a coordinate plane.