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
Using the given points (0,0) and (1,2), we can find the slope of the line passing through these two points.
The slope is calculated as the change in y divided by the change in x.
change in y = 2 - 0 = 2
change in x = 1 - 0 = 1
slope = change in y / change in x = 2 / 1 = 2
We can now use the slope-intercept form of a linear equation y = mx + b, where y is the y-value, x is the x-value, m is the slope, and b is the y-intercept.
Substituting the values (x, 24) and (2, 24) into the equation:
24 = 2x + b
To find the value of b, we can substitute the coordinates (0,0) into the equation:
0 = 0 + b
Therefore, the value of b is 0.
The equation of the line is y = 2x.
To find x when y = 24:
24 = 2x
Solving for x:
x = 24 / 2
x = 12
Therefore, the x-value of the point (x, 24) is 12.
The correct answer is B. 12.