Final answer:
The linear equation for Juan walking to school in 8 minutes covering 0.75 miles is represented by y = 0.09375x, where y is the distance in miles and x is the time in minutes.
Step-by-step explanation:
The linear equation that represents Juan walking to school in 8 minutes for a distance of 0.75 miles is based on the rate of change in distance over time. Since the rate of walking is constant, this forms a linear relationship between distance (miles) and time (minutes). The rate, or slope, m, can be found by the rise over run formula, which in this case is the distance divided by time.
To find the slope: m = distance/time = 0.75 miles / 8 minutes = 0.09375 miles/minute.
The linear equation can be written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Here, y represents the distance in miles and x represents the time in minutes. Since Juan starts from his home, the y-intercept, b, is 0 (since the distance from school when he starts is 0).
The linear equation representing this situation is:
y = 0.09375x
This equation indicates that for every additional minute Juan walks, he will have traveled another 0.09375 miles towards his school.