Question

1. answer the questions below based on the graph.

a) what is the constant of proportionality?
b) write an equation using the cop comparing the miles to hours.
c) how many miles would you travel in 18 hours?

1. solve and graph the following inequality.

-5x + 10 < -20

Explanation:

Step1: Find constant of proportionality

Pick a point (2,92). Calculate $\frac{\text{Distance}}{\text{Time}} = \frac{92}{2} = 46$

Step2: Write proportionality equation

Let $y$ = distance, $x$ = time. Equation: $y = 46x$

Step3: Calculate distance for 18 hours

Substitute $x=18$ into $y=46x$: $y = 46 \times 18 = 828$

Step4: Solve the inequality

Subtract 10 from both sides: $-5x + 10 - 10 < -20 - 10$ → $-5x < -30$
Divide by -5 (reverse inequality): $\frac{-5x}{-5} > \frac{-30}{-5}$ → $x > 6$

Answer:

a) 46
b) $y = 46x$ (where $y$ is distance in miles, $x$ is time in hours)
c) 828 miles
For the inequality $-5x + 10 < -20$:
Solution: $x > 6$
Graph description: Draw a number line, place an open circle at 6, and shade all values to the right of 6.