Final answer:
The slope of the line defined by the equation y = 2x - 3 is positive and represented by the coefficient of x in the equation, which is 2. This means the line rises 2 units for every 1 unit it moves to the right, making option (a) the correct answer.
Step-by-step explanation:
The student has asked about the slope of the line defined by the equation y = 2x - 3. In mathematics, the slope of a line is represented by the coefficient of x in its equation when the equation is in the slope-intercept form, which is y = mx + b where m stands for slope and b determines the y-intercept. Referring to the given equation y = 2x - 3, it is already in the slope-intercept form, so the coefficient of x, which is 2, represents the slope of the line.
Therefore, the slope of the line y = 2x - 3 is positive, and it implies that the line is inclined upwards as it moves from left to right on the Cartesian plane. For every increment of 1 unit on the horizontal axis, the line rises by 2 units on the vertical axis. Option (a) 2 is the correct answer to the question, indicating that the line has a positive slope and not a negative slope or a horizontal line at any value.