The relationship between hours studied ($h$) and test score ($s$) can be represented by a linear equation. Since each additional hour studied increases the test score by 5 points, starting from a base score of 50, the equation is:

$s = 50 + 5h$

where:

• $s$ is the test score,
• $h$ is the number of hours studied,
• 50 is the base score when no hours are studied,
• and 5 is the rate at which the score increases per hour studied.

Would you like further details on this, or do you have any questions?

Here are some related questions:

1. How would the equation change if each hour of study increased the score by 3 points instead of 5?
2. What would the test score be if a student studied for 10 hours?
3. How many hours would a student need to study to achieve a score of 90?
4. What is the y-intercept of this equation, and what does it represent in this context?
5. How would this equation change if the base score were 60 instead of 50?

Tip: In linear equations, the coefficient of the variable (like $5$ in $5h$) represents the rate of change in the dependent variable with respect to the independent variable.