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 6 B 12C 23D 25
To solve this problem, we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we can determine that the slope of the line is 2 gallons per minute. This means that for every minute that passes, the water level in the pool increases by 2 gallons.
To find how long it will take to fill the pool, we need to find the value of x when y (the water level) is 24 gallons.
Using the slope-intercept form of the equation, we have:
24 = 2x + b
To determine the value of b, we can substitute the coordinates (0, 0) into the equation:
0 = 2(0) + b
b = 0
So, the equation becomes:
24 = 2x
Solving for x, we have:
2x = 24
x = 24/2
x = 12
Therefore, the x-value of the point (x, 24) is 12.
The correct answer is B) 12.