We know that Car X travels 186 miles in 3 hours. We are asked to write an equation that describes the relationship between distance and time. We can assume that the equation has the following form.
y=mx
In this equation, x represents time and y represents the distance that Car X traveled after x hours. We want to find the value of m, which is the slope. We know that after x=3 hours the car travels y=186 miles. Let's substitute.
We found that the slope m is equal to 62. Now, we can write the equation that describes the relationship between distance and time for Car X.
y=mx ⇔ y=62x
We are asked to determine which of the given graphs represents the relationship between distance and time for Car X. First, let's look at Graph A. Notice that this graph does not cross the point (0,0).
Since Car X traveled 0 miles after 0 hours, its graph should cross the point (0,0). This means that Graph A does not represent the relationship between distance and time for Car X. Now, let's look at Graph B.
We can see that the slope of Graph B is equal to 213 divided by 3.
Slope of GraphB=213/3=71
In Part A, we found that the slope of the equation that represents the relationship between the distance and time of Car X is 62. Since Graph B has a different slope, Graph B cannot represent the relationship between distance and time for Car X. Let's look at Graph C.
The slope of Graph C is 248 divided by 4.
Slope of GraphC=248/4=62
The slope of Graph C is the same as the slope of the equation that we found in Part A. Also, Graph C crosses through the point (0,0). Therefore, Graph C represents the relationship between distance and time for Car X.
