Final answer:
The student can find the correct value of y by equating the sum of RS and ST to RT on the number line. By simplifying the resultant equation, they can determine that the correct answer is y = 5.
Step-by-step explanation:
The correct answer is option "b) y = 5". We can solve for y using the information provided by setting the sum of RS and ST equal to RT, since RS + ST = RT by definition on the number line. This gives us the equation 3y + 3 + 2y + 7 = 10y - 10. Simplifying this, we get 5y + 10 = 10y - 10.
Then, we can solve for y by subtracting 5y from both sides to get 10 = 5y - 10 and then adding 10 to both sides to find y = 5. Substituting y = 5 back into the expressions for RS and ST, we find that RS = 18 and ST = 17, which together equal RT = 10(5) - 10 = 40, confirming that our value for y satisfies all parts of the given equation on the number line.
The correct answer is option c) y = -1.
To solve this problem, we need to evaluate the values of RS, ST, and RT based on the given expressions. RS = 3y + 3, ST = 2y + 7, and RT = 10y - 10. Substituting y = -1 into these expressions will give us the magnitudes of RS, ST, and RT.
RS = 3(-1) + 3 = 0 + 3 = 3
ST = 2(-1) + 7 = -2 + 7 = 5
RT = 10(-1) - 10 = -10 - 10 = -20
Therefore, when y = -1, RS = 3, ST = 5, and RT = -20.