Final answer:
All the options listed by the student are linear equations because they adhere to the standard form of a linear equation, y = mx + b, where 'm' is the slope and 'b' is the y-intercept which is 0 in these cases.
Step-by-step explanation:
The student is asking to identify the equation of a line among several options. To determine which of the options represents a linear equation, we refer to the standard form of a linear equation, which is expressed as y = b + mx, where 'm' is the slope and 'b' is the y-intercept.
All of the options given are equations of a line as they follow the format of y = mx + b, where 'm' could be -1, 1, -5, or 5, and 'b' is implied to be 0 since it is not present. For example, option 1) y = -x can be rewritten as y = -1x + 0, which confirms that it is a linear equation. The same applies to the rest of the options, making them all valid linear equations.
Therefore, the answer to which equation(s) is/are linear among the options provided would be that all the listed equations are linear because they are all in the form of y = mx + b with the values of 'm' being -1, 1, -5, 5, -1, and 5, respectively.