Chapter 8.6, Problem 23E

To determine

To determine if the given data represents a linear, an exponential or a quadratic function and then write the function.

Answer to Problem 23E

  $y=-3x-2$

Explanation of Solution

Given information :

Here we can observe that there is a common difference of -3 in the given values of y , for the value of x.

Hence we can determine that this is a linear function.

Now we shall determine the function.

Take any two points on the function. Let’s take (0, -2) and (1, -5)

Equation by two points is given by the formula,

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

Put values we get,

  $\begin{array}{l}y-\left(-2\right)=\left(\frac{-5-\left(-2\right)}{1-\left(0\right)}\right)\left(x-0\right)\\ y+2=-3x\\ y=-3x-2\end{array}$