Question

Write and equation to represent the function.
Input(x). 1. 2. 3. 4
Output(y). 8. 19. 30. 41

Answer 1

Answer:

$y=11x-3$

Step-by-step explanation:

Given ordered pairs:

(1, 8)  (2, 19)  (3, 30)  (4, 41)

As the y is directly proportional to x (y values increase +11 for every +1 increase for the x-values) then the equation will be linear.

Point-slope form of a linear equation:  $y-y_1=m(x-x_1)$

(where $m$ is the slope and $(x_1,y_1)$ is a point on the line)

$\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}$

Let:

• $(x_1,y_1)=(1,8)$
• $(x_1,y_2)=(2,19)$

$\implies \textsf{slope }m=\dfrac{19-8}{2-1}=11$

Using point-slope equation with m = 11 and point (1, 8):

      $y-y_1=m(x-x_1)$

$\implies y-8=11(x-1)$

$\implies y=11x-3$