Chapter 12.CR, Problem 1CR

To determine

To graph:

The region of solutions of the given inequality $4x-5y>7$.

Answer to Problem 1CR

Solution:

The graph of the inequality $4x-5y>7$ is shown in figure $\left(1\right)$.

Explanation of Solution

Calculation:

Consider the given inequality.

$4x-5y>7$

Solve the linear inequality for the value of $y$.

$\begin{array}{c}4x-5y>7\\ -4x+5y<-7\\ y<\frac{4}{5}x-\frac{7}{5}\end{array}$

The associated equation is,

$y=\frac{4}{5}x-\frac{7}{5}$

The above equation is a line with slope $\frac{4}{5}$ and the $y$ intercept is $-\frac{7}{5}$.

Plot the graph for the equation $y=\frac{4}{5}x-\frac{7}{5}$. Greater than inequality sign is used so, plot this using a dashed line. The region of set of inequality is all the points below the line $y=\frac{4}{5}x-\frac{7}{5}$.

The region of solution for the given inequality is shown as shaded in graph below.

Conclusion:

Hence, the graph of the inequality $4x-5y>7$ is shown in figure $\left(1\right)$.