In simple linear regression, one can use the plot of residuals versus the fitted values of y to check for a constant variance as well as to make sure that the linear model is in fact adequate.

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This is a true statement. The plot of residuals versus the fitted values is known as a "residual plot" and can be used to check for violations of the assumptions of linear regression, including the constant variance assumption and the linearity assumption. If the plot shows a clear pattern (such as a funnel shape), it may indicate that the assumptions are being violated and the linear model is not appropriate.

In Simple Linear Regression, One Can Use the Plot of Residuals