Explanation:
- You can graph this situation by plotting the amount of slushy Sean drank over time, which means you'll need a linear function.
- On the x-axis, you can represent time in seconds, and on the y-axis, you can represent the amount of slushy in milliliters.
Best form of a line to use:
It's perhaps easier to graph the situation with the slope-intercept form, whose general equation is y = mx + b, where
- m is the slope (change in y / change in x),
- and b is the y-intercept (y-coordinate when x = 0).
Identifying the slope:
- Since Sean drank 5 milliliters of slushy each second, the slope is -5 as the volume decreased per each second and when the y-values decrease (loss of 5 mm) and the x-values increase (1 second added), the slope is negative.
Identifying the y-intercept:
- We're not explicitly told the y-intercept.
- However, we're told that Sean finished the slushy after 50 seconds.
- This means, the y-coordinate with an x-coordinate is 0 since a y-coordinate of 0 represents the slushy being depleted.
Thus, we can plug in (50, 0) for (x, y) and -5 for m in the slope-intercept form to find the y-intercept:
y = mx + b
0 = -5(50) + b
(0 = -250 + b) + 250
250 = b
Thus, the y-intercept is (0, 250), meaning Sean's slushy had a volume of 250 mm before he even began to drink it.
Therefore, the equation of the line modeling the situation is y = -5x + 250.
Creating the graph:
For the x-axis, my lowest value would be -60 while my highest at 60. This allows you to create a point at (50, 0) to show the time at which Sean finished his slushy on the line.
For the x-axis, I would make the ticks on the graph represent 10 units, meaning you'd only need 13 ticks in total.
For the y-axis, my lowest value would be -300 while my highest would be 300. This allows you to create a point at (250, 0) to show the y-intercept.
For the y-axis, I would make the ticks on the graph represent 50 units, meaning, you'd also only need 13 ticks in total.
I'll attach a graph from Desmos Graphing Calculator with the line y = -5x + 250 and the points (50, 0) and (0, 250)