Derive a set of inequalities to describe the region.
Triangle: vertices at (0, 0), (4, 0), (4, 5)

A) $\left\{ \begin{array} { c }
y \geq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
B) $\left\{ \begin{array} { c }
y \leq \frac { 5 } { 4 } x \
x \geq 4
\end{array} \right.$
C) $\left\{ \begin{array} { c }
y \geq \frac { 4 } { 5 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
D) $\left\{ \begin{array} { c }
y \leq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
E) $\left\{ \begin{array} { c }
y \leq \frac { 5 } { 4 } x \
x \leq 4
\end{array} \right.$

Question

Derive a set of inequalities to describe the region.  
Triangle: vertices at (0, 0), (4, 0), (4, 5)
 
A)  $\left\{ \begin{array} { c } 
y \geq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
B)  $\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \geq 4
\end{array} \right.$
C)  $\left\{ \begin{array} { c } 
y \geq \frac { 4 } { 5 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
D)  $\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$
E)  $\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \leq 4
\end{array} \right.$

Quizplus · Accepted Answer

The triangle's vertices suggest that the region is bounded below by $y = 0$ (the x-axis), to the right by $x = 4$, and above by the line connecting (4, 0) and (4, 5), which has a slope of $\frac{5}{4}$. The inequality $y \leq \frac{5}{4}x$ describes the area below this line, which matches the triangle's area. The conditions $y \geq 0$ and $x \leq 4$ ensure the region is within the first quadrant and to the left of $x = 4$, respectively.

Derive a Set of Inequalities to Describe the Region {y≥54xy≥0x≤4\left\{ \begin{array} { c } y \geq \frac { 5 } { 4 } x \\y \geq 0 \\x \leq 4\end{array} \right.⎩⎨⎧​y≥45​xy≥0x≤4​

Derive a Set of Inequalities to Describe the Region $\left\{ \begin{array} { c } y \geq \frac { 5 } { 4 } x \\y \geq 0 \\x \leq 4\end{array} \right.$