Questions: Graph the inequality subject to the nonnegative restrictions. 9x - 15y < 0, x ≥ 0, y ≥ 0

Transcript text: Graph the inequality subject to the nonnegative restrictions. \[ 9 x-15 y<0, x \geq 0, y \geq 0 \]

Solution

Solution Steps

Step 1: Rewrite the inequality in slope-intercept form

To rewrite the inequality $9x - 15y < 0$ in slope-intercept form, we isolate $y$:

$-15y < -9x$

$y > \frac{-9x}{-15}$

$y > \frac{3}{5}x$

Step 2: Identify the boundary line

The boundary line is $y = \frac{3}{5}x$. This is a line passing through the origin (0,0) with a slope of $\frac{3}{5}$. Since the inequality is $y > \frac{3}{5}x$, the boundary line should be dashed, and the region above the line should be shaded.

Step 3: Apply the nonnegative restrictions

The nonnegative restrictions $x \ge 0$ and $y \ge 0$ mean we are only considering the first quadrant of the Cartesian plane where both $x$ and $y$ values are nonnegative.

Step 4: Graph the inequality

Graph the line $y = \frac{3}{5}x$ as a dashed line. Shade the region above the line in the first quadrant.

Final Answer:

The graph of the inequality $9x - 15y < 0$ with the nonnegative restrictions $x \ge 0$ and $y \ge 0$ is the region above the dashed line $y = \frac{3}{5}x$ in the first quadrant.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!