The linear regression equation based on the data provided is:

$y = 1.4x - 35.5$

Using this equation, the projected test grade for a student with a homework grade of 55 is:

$y = 1.4(55) - 35.5 = 42$

So, the projected test grade is 42.

Do you need further details or have any questions? Here are five related questions to expand your understanding:

1. How is the slope of a linear regression equation interpreted in this context?
2. What does the intercept of the regression line represent?
3. How is the coefficient of determination (R²) useful in evaluating a regression model?
4. Can we use this linear model to predict test scores for homework grades outside the given range?
5. How does rounding affect the accuracy of the predicted results?

Tip: Always check the correlation coefficient to see how well the regression line fits the data.