Final answer:
The graph produced by an absolute value equation will be widest when the absolute value of the coefficient is smallest. Option B) y = -0.5|x| has the smallest absolute value of the coefficient and thus will produce the widest graph among the given options.
Step-by-step explanation:
The student is questioning about the width of the graph produced by different absolute value equations. The width of an absolute value graph is determined by the coefficient in front of the absolute value expression. This coefficient is often referred to as the stretch factor. A lower absolute value of the coefficient indicates a wider graph because it stretches the graph horizontally, whereas a higher absolute value of the coefficient indicates a narrower graph because it compresses it horizontally.
In the given options, the equation that produces the widest graph will have the smallest absolute value of the coefficient. Therefore, comparing the coefficients (2/3, -0.5, -2, and 1.5), we find that -0.5 has the smallest absolute value.
Thus, option B) y = -0.5|x| will produce the widest graph.