To determine the graph that corresponds to the given inequality, first, let's write the inequality for y:
[tex]2x\le5y-3[/tex]
Add 3 to both sides of the expression
[tex]\begin{gathered} 2x+3\le5y-3+3 \\ 2x+3\le5y \end{gathered}[/tex]
Divide both sides by 5
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le\frac{5}{5}y \\ \frac{2}{5}x+\frac{3}{5}\le y \end{gathered}[/tex]
The inequality is for the values of y greater than or equal to 2/5x+3/5, which means that in the graph the shaded area will be above the line determined by the equation.
Determine two points of the line to graph it:
-The y-intercept is (0,3/5)
- Use x=5 to determine a second point
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le y \\ \frac{2}{5}\cdot5+\frac{3}{5}\le y \\ 2+\frac{3}{5}\le y \\ \frac{13}{5}\le y \end{gathered}[/tex]
The second point is (5,13/5)
Plot both points to graph the line. Then shade the area above the line.
The graph that corresponds to the given inequality is the second one.
