Write the equation for this situation: the value, v, in hundreds of dollars, of Bob’s stamp collection is 12 dollars more than 1/3 of the age, t (in years).
Then graph the equation and use the graph to determine the value of Bob’s coin collection if it is 9 years old.
Please show all of your work.
v = (1/3)t + 12
to plot this, the easiest way (for me) is to get the x- and y-intercept (in this case, the x-axis = t-axis, and y-axis = v-axis).
to get t-intercept, we let v = 0 and solve for t:
v = (1/3)t + 12
0 = (1/3)t + 12
-(1/3)t = 12
t = -36
thus t-intercept is at (-36, 0)
to get v-intercept, we let t = 0 and solve for v:
v = (1/3)t + 12
v = 12
thus v-intercept is at (0, 12).
to plot, locate these points. connect them, and extend on both ends. you must plot this accurately since you need to find the value of v at t = 9.
hope this helps~ :)
To write the equation for this situation, we need to break down the problem into smaller parts.
First, we know that the value of Bob's stamp collection, v, is 12 dollars more than one-third of his age, t (in years). So we can start by setting up the equation:
v = (1/3)t + 12
This equation states that the value of Bob's stamp collection, v, is equal to one-third of his age, t, plus 12 dollars.
To graph this equation, we need to assign values to t and solve for v. Let's plug in a few values for t and solve for v:
When t = 0, v = (1/3)(0) + 12 = 12.
When t = 3, v = (1/3)(3) + 12 = 13.
When t = 6, v = (1/3)(6) + 12 = 14.
Now, let's plot these points (0, 12), (3, 13), and (6, 14) on a graph:
|
|
|
-2 | ● (0, 12)
-1 |
0 |
1 | ● (3, 13)
2 |
3 | ● (6, 14)
|________________________________
0 3 6 9 12
The graph is a straight line passing through these points.
To determine the value of Bob's coin collection when it is 9 years old, we can use the equation. Plug in t = 9 and solve for v:
v = (1/3)(9) + 12 = 15
According to the equation, Bob's coin collection would be valued at 15 hundreds of dollars when it is 9 years old.