Final answer:
To write the equation y = 1.6 - x as y = bx with 0 < b < 1, the negative slope must be addressed. In this context, the task is not feasible as written because multiplying by -1 does not give a positive coefficient less than 1 for x. Thus, it is not possible to convert y = 1.6 - x directly into the desired form without altering the properties of the equation.
Step-by-step explanation:
To rewrite the equation y = 1.6 - x in the form y = bx with 0 < b < 1, we start by noting that the equation is a linear equation. By the standard form y = mx + b, the slope is -1 and the y-intercept is 1.6. We are required to express the equation with a positive coefficient for x that is less than 1. To do this, we'll need to reverse the sign of the slope while preserving the equality.
We achieve this by multiplying the term -x by -1 and also multiplying the right side of the equation by -1 to maintain balance. This modification results in:
y = -1\(\cdot\)x \(\cdot\) -1
Thus, the equivalent equation in the desired form is y = 0.6x.
It is important to note that in this case, multiplication by -1 is necessary to get a positive coefficient for x. However, to satisfy the condition 0 < b < 1, we need to ensure that the value of -1 times whatever the coefficient of x presently is should be within that range. Here, it is evident that -1\(\cdot\)(-1) is 1, which does not meet the condition. A simple mistake to avoid is assuming that the negative sign can be flipped when looking for an equivalent equation with the given constraints.