Answer: There are two correct statements, which are:
b. the intersection (1,60) indicates the time in hours when celia and tayvin are the same distance from the city.
c. Celia drove at a faster rate than Tayvin.
Explanation:
The graph shows two linear functions with these characteristics and informations:
- dependent variable (vertical axis): distance traveled in miles)
- independent variable (horizontal axis): time (hours):
- inicial distance = y-intercept: (0,10) = 10 miles
- speed = slope = rise / run = [ 60 miles - 50 miles ] / [ 1 hour] =
speed = 50 miles / hour
- initial distance = y-intercept: (0,0) = 0
- speed = slope = rise / run = [60 miles - 0 miles] / [ 1 hour] =
= speed = 60 miles / hour
With that you can go over each answer choice to asses their validity:
a. Tayvin drove a faster rate than Celia.
FALSE. It was shown that Tayvin's speed was 50 miles/hour while Celia's speed was 60 miles/hour, hence Celia was 10 miles/hour faster than Tayvin.
b. the intersection (1,60) indicates the time in hours when Celia and Tayvin are the same distance from the city.
TRUE. The two lines intersect each other at the point with coordinates (1,60), where 1 is the time in hours and 60 is the distance in miles, meaning that both were at the same distance (60 miles) at the same time (1 hour).
c. Celia drove at a faster rate than Tayvin.
TRUE. As stated before, Celia drove 10 miles/hour faster than Tayvin
d. the intersection (1,60) indicates the time in hours when celia and tayvin are traveling at the same speed.
FALSE. As stated in the point b., the intersection point indicates the time in hours when Celia and Tayvin are the same distance from the city; the speed were different all the time, since both kept thier respective uniform speeds (constant slope means constant speed).
