Chapter 4.3, Problem 9Q

To determine

To calculate: To write the linear function

Answer to Problem 9Q

Thelinear function is $y=5x+13$

Explanation of Solution

Given: $f\left(-3\right)=-2;f\left(-2\right)=3$

Formula Used:

Equation of line in slope intercept form is given as:

  $y=mx+c$ , where $\begin{array}{l}m=slope\\ c=y-intercept\end{array}$

Also, equation of line passing through two points is given as

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

Calculation:

Given that values of linear function as follows:

  $f\left(-3\right)=-2;f\left(-2\right)=3$

This means that at $x=-3$ , $y=-2$ and $x=-2$ , $y=3$

Equation of function is found by finding the equation of line passing through $\left(-3,-2\right)$ and $\left(-2,3\right)$

Thus, equation of line is calculated as follows:

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

Substituting the values in above equation:

  $\begin{array}{l}y-3=\frac{-2-3}{-3-\left(-2\right)}\left(x-\left(-2\right)\right)\\ y-3=\frac{-5}{-3+2}\left(x+2\right)\\ y-3=\frac{-5}{-1}\left(x+2\right)\\ y-3=5x+10\\ y=5x+13\end{array}$

Conclusion:

Hence, the linear function is $y=5x+13$