Question

dominick is training for a race. he spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. this week, he spent more than 6 hours training for the race. which graph represents his possible training times this week?

Explanation:

Step1: Define variables

Let $x$ = number of runs, $y$ = number of swims.

Step2: Set up inequality

Total training time > 6 hours:
$0.75x + 1.5y > 6$

Step3: Simplify the inequality

Divide all terms by 0.75:
$x + 2y > 8$
Rearrange to slope-intercept form:
$y > -\frac{1}{2}x + 4$

Step4: Analyze graph requirements

• Boundary line: $y = -\frac{1}{2}x + 4$ (dashed, since inequality is strict)
• Shaded region: Above the line (since $y >$ expression)
• Intercepts: When $x=0$, $y=4$; when $y=0$, $x=8$

Answer:

The first graph (top-left, with x-axis up to 9, y-axis up to 5, shaded region above the line connecting (0,4) and (8,0))