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The process for checking if the equipment is measuring linearly requires taking measurements at three distinct value points. This approach allows for a comprehensive assessment of the instrument's response across a range of values, rather than just at a single point. By evaluating measurements at various levels, one can determine if the output of the instrument changes proportionally with different input values, which is a hallmark of linearity.

When measuring at a single point, consistency might indicate reliability but does not provide information on how the instrument performs at other points along the scale. Verifying three different instruments' readings could give insights into instrument variability, but it does not specifically test linearity of the measurement of one instrument. Similarly, repeating the same measurement multiple times would check for precision and consistency, not linearity across varying levels. Thus, measuring at three distinct value points is the methodological approach that effectively confirms the linear response of the equipment.