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Answer:
Here is the summary of true statements:
A) The statement of the function modeled is (0, 3) is TRUE.
D) the equation for the line function is y = 2x+3 is TRUE.
E) the given table represents the linear function is TRUE
Step-by-step explanation:
Given the table
x 1 3 5 7
y 5 9 13 17
E)
It is clear that there is a CONSTANT CHANGE in the x and y values of the graph.
THE CONSTANT CHANGE IN X VALUES
i.e. 3-1=2, 5-3=2, 7-5=2
THE CONSTANT CHANGE IN Y VALUES
i.e. 9-5 = 4, 13 - 9 = 4, 17 - 13 = 4
Thus, the given table represents the linear function is TRUE
B)
It is clear that the value of y increase as the value of x increases.
Thus, the statement ''the value of y decreases as the value of x increases'' is FALSE!
D)
We know that the slop-intercept form of the line equation is
where m is the slope and b is the y-intercept.
Determining the equation
Taking two points
(1, 5)
(3, 9)
Finding the slope between (1, 5) and (3, 9)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [9 - 5] / [3 - 1]
= 4 / 2
= 2
Thus, the slope of the line = m = 2
now substituting m = 2 and the point (1, 5) to determine the y-intercept
y = mx+b
5 = 2(1) + b
b = 5-2
b = 3
Thus, the value of y-intercept b = 3
substituting b = 3 and m = 2 in the slope-intercept form
y = mx+b
y = 2x+3
Therefore, the equation for the line function is y = 2x+3 is TRUE
A)
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
We already know that the y-intercept b = 3
It means the y-intercept modeled is (0, 3)
Therefore, the statement of the function modeled is (0, 3) is TRUE.
C)
We have already got the equation
y = 2x+3
substituting x = 8
y = 2(8)+3
y = 10+3
y = 13
so at x = 8, the value of y = 13
Therefore, the statement that the ''On a graph of the function when x = 8, the value of y will be 2'' is FALSE!
Conclusion:
Here is the summary of true statements:
A) The statement of the function modeled is (0, 3) is TRUE.
D) the equation for the line function is y = 2x+3 is TRUE.
E) the given table represents the linear function is TRUE