Final answer:
The slope of line b would be the same as that of line a, which is 2, because parallel lines always have identical slopes. The correct answer to the question is b) 2, as parallel lines must have the same slope, regardless of their y-intercepts.
Step-by-step explanation:
The question asks about the slope of line b given that line a is parallel to line b and that the slope of line a is 2. In mathematics, particularly in the study of linear equations, the slope of a line is a measure of how steep the line is. When two lines are parallel, they have the same slope. Therefore, if line a is parallel to line b and has a slope of 2, then the slope of line b must also be 2.
Understanding Slope is crucial in interpreting linear equations. The slope (represented by 'm' in the equation of a line) describes the rate at which the dependent variable changes in relation to the independent variable. For any linear equation, the slope is the same all along a straight line, as indicated by the rise over the run. The y-intercept (represented by 'b') is where the line crosses the y-axis, but this is not relevant to matching slopes between parallel lines.
Thus, the correct answer to the question is b) 2, as parallel lines must have the same slope, regardless of their y-intercepts.