Chapter 7, Problem 5CA

To determine

To graph:To graph the given equation in a coordinate plane, check whether the equation represents linear or non-linear function and its domain is continuous or discrete.

Answer to Problem 5CA

Equation represents a linear function.

Domain is continuous.

Explanation of Solution

Given information:Equation is $y=-\frac{1}{3}x+2$ .

Calculation:

• Putting $x=-6$ in given equation,

  $\begin{array}{l}y=-\frac{1}{3}(-6)+2\\ y=4\end{array}$

Similarly putting some other values and arranging the results in a table,

  $\begin{array}{llllllll}x\hfill & -6\hfill & -4\hfill & -2\hfill & 0\hfill & 2\hfill & 4\hfill & 6\hfill \\ y\hfill & 4\hfill & \frac{10}{3}\hfill & \frac{8}{3}\hfill & 2\hfill & \frac{4}{3}\hfill & \frac{2}{3}\hfill & 0\hfill \end{array}$

Plotting the graph using values in table,

  

  

• It is evident from the graph that the graph of the equation is a line and has a constant slope, moreover, the highest exponent of the equation is $1$ .

  $\therefore$ Equation represents a linear function.

• As y is defined on whole of the real line,
Domain $=(-\infty ,\infty )$

  $\therefore$ Domain is continuous.