Question

Consider the two functions below. Which one of these functions is linear? What is its equation? Enter any answers to two decimal places.

Answer 1

Answer:

$y = 1.67x$

Step-by-step explanation:

Function A:

x  || 3  ||  6  ||  9  ||  12  ||  15

y  || 5  ||  10 ||  15 ||  20 || 25

See attachment for Function B

First, we need to determine the equation of function A using linear interpolation

As follows:

$y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}$

Take any two corresponding values of x and y to be:

$(x_1,y_1) = (3,5)$

$(x_2,y_2) = (15,25)$

The equation becomes:

$y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}$

$y = 5 + (x - 3)\frac{25 - 5}{15 - 3}$

$y = 5 + (x - 3)\frac{20}{12}$

$y = 5 + (x - 3)\frac{5}{3}$

Open bracket

$y = 5 + \frac{5x}{3} - \frac{5*3}{3}$

$y = 5 + \frac{5x}{3} - 5$

Collect Like Terms

$y = \frac{5x}{3} - 5 + 5$

$y = \frac{5x}{3}$

$y = 1.67x$

This function is linear and there is no need to check for function B