felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. he…

felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. he spent less than $10. which graph represents this scenario?

felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. he spent less than $10. which graph represents this scenario?

Answer

Explanation:

Step1: Write the inequality

The cost of grapes is $1.25x$ and the cost of cereal is $2.5y$. Since he spent less than $10$, the inequality is $1.25x + 2.5y<10$.

Step2: Rewrite the inequality in slope - intercept form

Divide the entire inequality by $2.5$: $\frac{1.25x}{2.5}+\frac{2.5y}{2.5}<\frac{10}{2.5}$, which simplifies to $0.5x + y<4$, or $y < - 0.5x+4$. The boundary line $y=-0.5x + 4$ has a $y$-intercept of $4$ and a slope of $-0.5$. Also, since the inequality is $y < - 0.5x + 4$, the line is dashed and the shading is below the line.

Answer:

The graph with a dashed line having a $y$-intercept of $4$ and a negative slope (going down - ward from left to right) and shading below the line.