Final Answer:
y can take any value from 3 to 7, inclusive.
Step-by-step explanation:
Given equation is y=2x+3, and x<2. Since x is lesser than 2, it can take any value from -∞ to 2, exclusive. Therefore, substituting x in the equation gives y values from 3 to 7, inclusive. Mathematically, this can be expressed as: y = 2(-∞ to 2) + 3 = 3 to 7.
To explain in more detail, when x = -∞, y = 3. Similarly, when x = -1, y = 5; when x = 0, y = 7; and when x = 2, y = 9. Since x is only allowed to take values between -∞ and 2, exclusive, y can only take values from 3 to 7, inclusive.
Furthermore, we can also derive this answer by considering the slope of the line, that is 2, and the y-intercept, which is 3. The slope of the line shows that for every increase of one in x, y will increase by two. Similarly, the y-intercept shows that even when x is at 0, y will still be 3. This further reinforces the fact that y can only take values from 3 to 7, inclusive.
In conclusion, it can be determined that when the equation y=2x+3 and x<2, all the possible values of y are from 3 to 7, inclusive.