Chapter SH, Problem 9.7.6EP

To determine

The representation of the equation $-2x+5y=10$ is either linear or non-linear is to be analyze.

Answer to Problem 9.7.6EP

The eq. $-2x+5y=10$ shows the representation of the linear function

Explanation of Solution

Given:

  $-2x+5y=10$

Concept Used:

In mathematics, a polynomial equation of the one degree that can be put in the form of the equation $f\left(x\right)=mx+b$ , then the function is known as the linear function. The graph of the linear function is always straight line.

A mathematical system of equation which is combine form of two or more variables which contains at least one equation which is not linear is known as the non-linear function.

Calculation:

The given equation is rewrite in the form of the straight line eq.:

  $\begin{array}{l}-2x+5y=10\\ y=\frac{2}{5}x+\frac{10}{5}\\ y=\frac{2}{5}x+2\end{array}$

The equation of straight line is

  $y=mx+b$

Compare the given eq. $y=\frac{2}{5}x+2$ with the straight line eq.:

  $m=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.,b=2$

That means the graph drawn by this eq. is a straight line which is passing through $y$ -intercept $2$ with the slope of $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ .

The given eq. shows the representation of the linear function.

Conclusion:

Hence, $-2x+5y=10$ is linear function.