A water balloon is thrown from a window. The height of the balloon can be found using the equation
y = -7.5x + 45, where x is the time in seconds the balloon has been in the air.
The equation y = -7.5x + 45 represents the height of the water balloon as a function of time. In this equation, y represents the height of the water balloon in meters, and x represents the time in seconds since the balloon has been in the air.
The equation is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -7.5 and the y-intercept is 45.
The slope of -7.5 indicates that for every second the balloon is in the air, its height decreases by 7.5 meters. The negative slope indicates that the height of the balloon is decreasing over time.
The y-intercept of 45 represents the initial height of the balloon when it was thrown, which is 45 meters in this case. This means that at x = 0 (when the balloon was just thrown), the height of the balloon is 45 meters.
To find the height of the balloon at a specific time, substitute the value of x into the equation and solve for y. For example, if we want to find the height of the balloon after 5 seconds, we substitute x = 5 into the equation:
y = -7.5(5) + 45
y = -37.5 + 45
y = 7.5
Therefore, after 5 seconds, the height of the balloon is 7.5 meters.
how many seconds did it take to hit the ground
To find the number of seconds it took for the water balloon to hit the ground, we can set the height, y, equal to 0 and solve for x.
0 = -7.5x + 45
To isolate x, we can subtract 45 from both sides of the equation:
-45 = -7.5x
Dividing both sides of the equation by -7.5:
x = 6
Therefore, it took 6 seconds for the water balloon to hit the ground.