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Genesis's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation 
y=6.3 x+66, where 
y represents the expected quiz score and 
x represents hours spent on homework that week. What is the meaning of the 
x-value when 
y=90 ?
A student's expected quiz score if they spent 1 hour on their homework.
A student's expected quiz score if they spent 90 hours on their homework.
The change in expected quiz score for every additional one hour students spend on their homework.
The number of hours a student should spend on their homework to expect a score of 90 on the quiz.

Genesis's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=6.3x+66 y=6.3 x+66 , where y y represents the expected quiz score and x x represents hours spent on homework that week. What is the meaning of the x x -value when y=90 y=90 ?\newlineA student's expected quiz score if they spent 11 hour on their homework.\newlineA student's expected quiz score if they spent 9090 hours on their homework.\newlineThe change in expected quiz score for every additional one hour students spend on their homework.\newlineThe number of hours a student should spend on their homework to expect a score of 9090 on the quiz.

Full solution

Q. Genesis's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=6.3x+66 y=6.3 x+66 , where y y represents the expected quiz score and x x represents hours spent on homework that week. What is the meaning of the x x -value when y=90 y=90 ?\newlineA student's expected quiz score if they spent 11 hour on their homework.\newlineA student's expected quiz score if they spent 9090 hours on their homework.\newlineThe change in expected quiz score for every additional one hour students spend on their homework.\newlineThe number of hours a student should spend on their homework to expect a score of 9090 on the quiz.
  1. Understand Equation and Question: Understand the equation and what is being asked.\newlineThe equation y=6.3x+66y=6.3x+66 represents a linear relationship between the time spent on homework (xx) and the expected quiz score (yy). We need to find the meaning of the xx-value when y=90y=90.
  2. Set Up Equation with y=90y=90: Set up the equation with y=90y=90.\newlineTo find the xx-value when y=90y=90, we substitute 9090 for yy in the equation.\newline90=6.3x+6690 = 6.3x + 66
  3. Solve for x: Solve for x.\newlineSubtract 6666 from both sides of the equation to isolate the term with xx.\newline9066=6.3x90 - 66 = 6.3x\newline24=6.3x24 = 6.3x
  4. Divide to Find x: Divide both sides by 6.36.3 to find the value of xx.\newlinex=246.3x = \frac{24}{6.3}\newlinex3.81x \approx 3.81
  5. Interpret the Result: Interpret the result.\newlineThe xx-value of approximately 3.813.81 represents the number of hours a student should spend on their homework to expect a score of 9090 on the quiz. This answers the question prompt.

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