Sam wants to know how long it will take to fill his baby pool that holds 24 gallons. After 1 minute, there are 2 gallons of water in the pool. He plots the points (0,0) and (1,2) on his coordinate plane. What is the x-value of the point (x, 24)?
Responses
A 66
B 1212
C 2323
D 25
We can use the formula for the slope of a line to find the x-value of the point (x, 24).
The slope of a line is equal to rise over run. In this case, the rise is the change in y-values (from 0 to 24), and the run is the change in x-values (from 0 to x).
The slope of the line passing through the points (0,0) and (1,2) is (2-0)/(1-0) = 2/1 = 2.
Since the line passes through the point (0,0), we can use the point-slope form of a line to find the equation:
y - 0 = 2(x - 0)
Simplifying, we get:
y = 2x
To find the x-value of the point (x, 24), we can substitute y = 24 into the equation:
24 = 2x
Solving for x, we get:
x = 24/2 = 12
So the x-value of the point (x, 24) is 12.
Therefore, the correct answer is B) 12.