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.
X,0,1,2,3
y,5,8,11,14
Question content area bottom
Part 1
Represent the relationship using words. Choose the correct answer below.
A.
The value of y is
nine
less than the quantity
ten times the value of x.
B.
The value of y is the
square of the quantity
ten
plus the value of x.
C.
The value of y is
two times the value of x.
D.
The value of y is the
cube of the quantity
one
minus the value of x.
E.
The value of y is
five
more than the quantity
three times the value of x.
Your answer is correct.
F.
The value of y is
six
less than the
square of the quantity
three times the value of x.
Part 2
Represent the relationship using an equation.
y
=
enter your response here
(Simplify your answer. Type an expression using x as the variable.)
The relationship can be represented using the equation:
y = 3x + 5
Part 3
Represent the relationship using a graph.
The graph would be a straight line that starts at the point (0, 5) and has a slope of 3. The x values would be plotted on the x-axis and the corresponding y values would be plotted on the y-axis.
Is the relationship a linear function?
Yes
No
Yes, the relationship is a linear function because it can be represented by a straight line.
Part 1: The relationship can be represented using words as follows:
E. The value of y is five more than the quantity three times the value of x.
Part 2: The relationship can be represented using an equation as follows:
y = 3x + 5
To determine whether the relationship is a linear function, we can check if the differences in y-values are constant. Calculating the differences in y-values:
8 - 5 = 3
11 - 8 = 3
14 - 11 = 3
Since the differences between consecutive y-values are constant, the relationship is a linear function.