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,3,11,19,27
Represent the relationship using words. Choose the correct answer below.
A.
The value of y is
four
less than the
cube of the quantity
ten times the value of x.
B.
The value of y is
eight
less than the quantity
six times the value of x.
C.
The value of y is
ten times the value of x.
D.
The value of y is the
square of the quantity
one
minus the value of x.
E.
The value of y is the
cube of the quantity
one
plus the value of x.
F.
The value of y is
three
more than the quantity
eight times the value of x.
Your answer is correct.
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 equation representing the relationship is y = 8x + 3
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
x
y
0
5
1
8
2
11
3
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 words as: "The value of y is five more than three times the value of x."
The equation representing the relationship is y = 3x + 5.
To represent the relationship using words, we can observe that the value of y is increasing by 8 for each increase of 1 in x. The relationship can be described as: "The value of y is eight less than the quantity six times the value of x."
To represent the relationship using an equation, we can use the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. To find the slope, we calculate the difference in y-coordinates divided by the difference in x-coordinates:
m = (11 - 3) / (1 - 0) = 8 / 1 = 8
Now, we can choose any point on the line, for example, (0, 3), and substitute the values into the equation along with the calculated slope:
y = 8x + c
Plugging in the values for (0,3), we get:
3 = 8(0) + c
3 = 0 + c
c = 3
Therefore, the equation representing the relationship is:
y = 8x + 3