how do i solve this? **Interactive Question: Understanding Linear Functions****Your answer is incorrect.****Question:**Could the data represent a linear function? If so, give the rate of change.\[\begin{array}{c|cccc}x & 3 & 6 & 9 & 12 \\\hlinef(x) & 4 & 22 & 40 & 58 \\\end{array}\]**Instructions:**If the data could not represent a linear function, enter NA.**Your Task:** Calculate the Rate of Change: \[ \text{Rate of change} = \_\_\_\_ \]**Resources:**- eTextbook and Media- **Hint**: (Click for assistance)**Status:**- **Attempts: 1 of** (unlimited, if applicable)**Options:**- Save for Later

Name: how do i solve this? **Interactive Question: Understanding Linear Func
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: how do i solve this? **Interactive Question: Understanding Linear Functions****Your answer is incorrect.****Question:**Could the data represent a linear function? If so, give the rate of change.\[\begin{array}{c|cccc}x & 3 & 6 & 9 & 12 \\\hlinef(x) &

Given that: The table ,By using , Linear Function in Function Notation : Function notation is an equation written in the form knows a s slope - intercept form of a line , where x is the input value a, m is the rate of change and b is the initial value of the dependent variable . Slope - intercept form is f (x) = m x + b. Rate of change = f ( x2 ) - f ( x1)x2 - x1 .To express the given equation in the format f(x) = mx + b. To find the change in f(x) : Change in f(x) = f(x 2 ) - f ( x 1 ) = 22- 4 = 18 f ( x 3 ) - f ( x 2 ) = 40 - 22 = 18 f ( x 4 ) - f( x 3 ) = 58 - 48 = 18 To find change in x : Change in x = x 2 - x 1 = 6 - 3 = 3 x 3 - x 2 = 9 - 6 = 3 x 4 - x 3 = 12 - 9 = 3 To get, Change in f (x) = 18 and Change in x = 3 . Slope ( m) = change in f (x)change in x = 183 = 6 To get , Rate of change ( m) = 6. Plug the value m = 6 in the above formula, f ( x) = 6x + b. To find b : Take the point ( x, f (x) ) =( 3, 4) from the table. Plug x = 3 and f (x) = 4 in the equation f ( x) = 6x + b. To get, 4 = 6 ( 3) + b Solve for b: 4 = 18 + b b = - 14 To get, f (x )= 6 x + b = 6 x - 14 Then, f ( x) = 6 x - 14 Therefore, The data represent the linear function is f ( x) = 6x - 14. Rate of change = 6.