Problema Solution
A person is driving a car on a straight road. The graph shows the distance y miles that the individual is from home after x hours. Find the slope-intercept form of the line. How fast is the car traveling? How far was the individual from home initially? How far was the individual from home after 3 hours and 15 minutes? The graph shows (1, 35) (3,95).
Answer provided by our tutors
The graph is the line trough (1, 35) and (3, 95)
The slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept
m = (95 - 35)/(3 - 1)
m = 30
y = 30x + b
since it goes trough (1, 35) we have for x = 1, y = 35
35 = 30*1 + b
b = 35 - 30
b = 5
the slope intercept form of the line is y = 30x + 5
How fast is the car traveling?
v = (95 - 35)/(3 - 1)
v = 30 mph
How far was the individual from home initially?
Initially for x = 0 the individual was y = 5 miles away from home.
How far was the individual from home after 3 hours and 15 minutes?
After 3 hr and 15 min = 3.25 hr or x = 3.25 hr the individual was y = 3.25*30 + 5 = 102.5 miles away from home.