Question

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

х
0
1
2.
3
4
- 6
- 9
12
- 15
18
O quadratic; y = -x2 + 2x - 6
linear; y = - 3x -6
O quadratic; y = 32 - 2x
exponential; y = -6•1.5%

Answer 1

Option (2).

Explanation:

From the figure attached,

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

`y_(2)-y_(1)=-9-(-6)`

= -3

`y_(3)-y_(2)=-12-(-9)`

= -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' =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

m =
`(-9+6)/(1-0)` = -3

Y-intercept 'b' = -6

Equation of the line will be,

y = -3x - 6

Option (2) will be the answer.