Question

a patient is not allowed to have more than 270 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 135 milligrams of cholesterol. each ounce of meat provides 90 milligrams of cholesterol. completes parts (a) through (c) below. the inequality is 135x + 90y ≤ 270. (use integers or decimals for any numbers in the expression.) b. graph the inequality. because x and y must be positive, limit the graph to quadrant i only. choose the correct graph below. a. graph with shaded region b. graph with shaded region c. graph with shaded region d. graph with shaded region

Explanation:

Step1: Rewrite the inequality in slope - intercept form

Starting with $135x + 90y\leq270$, solve for $y$. First, subtract $135x$ from both sides: $90y\leq - 135x + 270$. Then divide by 90: $y\leq-\frac{135}{90}x+\frac{270}{90}$, which simplifies to $y\leq-\frac{3}{2}x + 3$.

Step2: Find the x - intercept

Set $y = 0$ in the equation $y=-\frac{3}{2}x + 3$. Then $0=-\frac{3}{2}x+3$. Add $\frac{3}{2}x$ to both sides: $\frac{3}{2}x=3$. Multiply both sides by $\frac{2}{3}$ to get $x = 2$.

Step3: Find the y - intercept

Set $x = 0$ in the equation $y=-\frac{3}{2}x + 3$. We get $y=3$.

Step4: Determine the shading

Since the inequality is $y\leq-\frac{3}{2}x + 3$, we shade the region below the line $y =-\frac{3}{2}x+3$ in the first - quadrant (because $x\geq0$ and $y\geq0$). The line $y=-\frac{3}{2}x + 3$ is a solid line because the inequality is $\leq$.

The correct graph has a solid line with a $y$ - intercept of 3 and an $x$ - intercept of 2, and the shaded region is below the line in the first - quadrant.

Answer:

D. (assuming that graph D is the one that matches the above - described characteristics)