Question

1.

Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.


A. exponential; y = –6 • 1.5x


B. quadratic; y = –x2


C. exponential; y = 6 • 2.5x


D. linear; y = –3x – 6

Answer 1

D. linear; y = –3x – 6

B. quadratic; y = –x2

Explanation:

Let

A (0,-2) B (1,-3) C (2,-4) D ( 3,-5) E (4,-6)

using a graph tool

see the attached figure N 1

case a) exponential

see the attached figure N 2

case b) quadratic

see the attached figure N 3

case c) linear

see the attached figure N 4

case d) linear

see the attached figure N 5

therefore

the answer is

the case c) linear

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Answer:

For the first part

What type of function best models the data in the graph?

✔ quadratic

y = 0.433x2 for the second part.

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Answer:

Option (2).

Step-by-step explanation:

From the figure attached,

Since there is a common difference in each successive term and previous term of y,

= -3

= -3

Therefore, this data represents a linear equation.

Now we choose two points from the table given.

Let the points are (0, -6) and (1, -9)

Slope of this line 'm' =

m = = -3

Y-intercept 'b' = -6

Equation of the line will be,

y = -3x - 6

Option (2) will be the answer.

Answer 2

By looking at the graph, it's evident that the data follows a linear trend. Therefore, the best-fitting model is a linear function. The correct choice is: D. linear; y = -3x - 6. This equation represents a linear relationship where the coefficient of x is -3, and the constant term is -6.

The given data exhibits a linear relationship, as the y-values decrease by a constant amount (3) for each increase in x by 1.

This pattern suggests a linear function. The correct model is a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the data is well-described by the linear equation y = -3x - 6, with a slope of -3 and a y-intercept of -6.

This linear model accurately represents the consistent decrement in y-values corresponding to the incremental increase in x-values in the given dataset.

The correct answer is option D.