Final answer:
The slope of the ice's mass over time graph is -15 g/min, the y-intercept is 1125 g, and the x-intercept, also known as zero, occurs at 75 min which signifies the time when all the ice is melted.
Step-by-step explanation:
To determine the slope, y-intercept, and x-intercept for the graph of the mass of the ice as it melts over time, we start with the given information: the initial mass of the ice is 1125 g and it decreases by 15 g each minute. When we graph the mass of the ice against time, we get a linear function, where the mass is the dependent variable (y-axis) and time is the independent variable (x-axis).
The slope of the line represents the rate of change of the ice's mass over time, which in this case is a loss of 15 g/min. Therefore, the slope is -15 g/min.
The y-intercept is the value of the ice's mass at time t=0, which is the initial mass of the ice, 1125 g.
We find the x-intercept by setting the linear equation to zero (when the ice is fully melted) and solving for time. The equation for this scenario would be: Mass = 1125 g - 15 g/min × Time. To find when the mass is zero, set the equation to 0 and solve for time, which gives us 0 = 1125 g - 15 g/min × Time. Dividing both sides by -15 g/min we find that Time = 1125 g / 15 g/min = 75 min.
Therefore, the zero or the x-intercept is 75 minutes, indicating that all the ice would melt after 75 minutes under the controlled conditions.