Final answer:
The student's question involves determining the characteristics of straight lines in algebra, specifically their slopes and y-intercepts, using the equations provided. Each line equation can be analyzed to identify its slope and y-intercept, which define the line's shape and position on a coordinate plane.
Step-by-step explanation:
The question given by the student pertains to the field of Mathematics, specifically to the Algebra of Straight Lines. Each equation provided represents a straight line in a two-dimensional coordinate system. Line 1 is y = -3/2x - 1, Line 2 is 2y = -3x + 7 (which can be rewritten as y = -3/2x + 7/2 after dividing both sides by 2), and Line 3 is 4x - 6y = -8 (which simplifies to y = 2/3x + 4/3 after rearranging and dividing).
For each of these lines, the slope (represented by 'm') and the y-intercept (represented by 'b') are fundamental characteristics that determine the line's shape and position. The slope indicates how steep the line is, while the y-intercept indicates where the line crosses the y-axis. In the context of this student's question, understanding how to identify these parameters from the equation of a line is crucial.
For a line represented by the equation y = mx + b, the coefficient of 'x' corresponds to the slope (m), and the constant term corresponds to the y-intercept (b). For example, using the provided references such as Figure A1, one can understand that in the equation y = 9 + 3x, the slope is 3, and the y-intercept is 9.