Answer and explanation:
Background info:
- Slope is defined as the change in y values / change in x.
- The y-intercept is the point on a graph where a line intercepts the y-axis (also defined algebraically as y when x = 0)
- It is an essential part of a linear equation, whose general formula is:
y = mx + b, where,
- m is the slope and,
- b is the y-intercept
If we look at the y-values in the table, we see that 4 ounces is added each time (16 + 4 = 20 + 4 = 24...). Similarly, if we look at the x-values in the table, we see that 0.5 hours is added each time (0 + 0.5 = 0.5 + 0.5 = 1 ...).
Therefore, since the change in y is 4 (oz) and the change in x is 0.5 (hr), we divide 4 by 0.5 to find the slope:
4 / 0.5 = 8 = m
As we can see on the table, when x is 0, y = 16. Thus, 16 is our y-intercept.
Thus, the general equation for the table is y = 8x + 16
Interpreting the slope and y-intercept: When we consider our units, slope in context of this problem is change in ounces / change in hours. We can think of 8 as the fraction 8 over 1.
- Slope: Thus, for 1 additional hour that passes, 8 ounces of water is consumed
- When 0 hours have passed, 16 ounces of water is consumed. Thus, before the work even begins, the individual drinks 16 ounces of water