Question

Alexander's math teacher finds that there's roughly a linear relationship between theamount of time students spend on their homework and their weekly quiz scores. Thisrelationship can be represented by the equation y = 6.9x + 65, where y representsthe expected quiz score and x represents hours spent on homework that week. Whatis the meaning of the x-value when y 88?

Answer 1

We have an expression that relates scores (y) and homework hours (x).

The expression is:

$y=6.9x+65$

If we know that y=88, it means that the quiz score was 88. We can estimate how many hours of homework correspond to this score by replacing y with 88 in the equation and solve for x:

$\begin{gathered} y=6.9x+65=88 \\ 6.9x+65=88 \\ 6.9x=88-65 \\ 6.9x=23 \\ x=\frac{23}{6.9} \\ x\approx3.33 \end{gathered}$

When y=88, x has a value of 3.33, meaning that, to get that score of 88, the amount of hours of homework were 3.33 hours according to the relation find by the math teacher.

Answer: x=3.33 hours of homework, correspond to a score of 88, according to the linear relation.