Question

1. rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. after 2 hours, she is 13 mi from the campground. after four hours, she is 6 mi from the campground. the equation ( y = -3.5x + 20 ) represents rachel’s hike. what is the slope and y - intercept of the graph, and what do they represent?

Explanation:

Step1: Identify slope-intercept form

The standard slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Match given equation to form

Compare $y = -3.5x + 20$ with $y = mx + b$. Here, $m = -3.5$ and $b = 20$.

Step3: Interpret slope

The slope $-3.5$ is the rate of change of distance to the campground. It means Rachel's distance to the campground decreases by 3.5 miles each hour (her hiking speed is 3.5 mph toward the campground).

Step4: Interpret y-intercept

The y-intercept $20$ is the value of $y$ when $x=0$ (time = 0 hours). This is the initial distance from the ranger station to the campground, 20 miles.

Answer:

• Slope: $-3.5$; it represents Rachel's hiking rate: her distance to the campground decreases by 3.5 miles per hour (or her hiking speed is 3.5 mph toward the campground).
• Y-intercept: $20$; it represents the initial total distance from the ranger station to the campground, which is 20 miles (the distance to the campground at the start of the hike, when $x=0$ hours).