Final answer:
Linear equations in two-dimensional space are graphed on a coordinate system with x and y axes. Systems of linear equations can have one solution (lines intersecting at one point), no solution (parallel lines), or infinite solutions (coinciding lines). The slope and y-intercept of a line determine its position and orientation in the coordinate system.
Step-by-step explanation:
The concepts described in the question pertain to linear equations and their graphical representations in a two-dimensional space. In such a space, the most convenient coordinate system for these problems is one with perpendicular axes, typically called the x-axis (horizontal) and the y-axis (vertical).
A system of equations with one solution will have lines that intersect at exactly one point, indicating they have different slopes. In contrast, a system with no solution includes lines that are parallel and therefore never intersect, as they have the same slope but different y-intercepts. Lastly, a system with infinite solutions will have coinciding lines, which means the lines are identical and have the same slope and y-intercept, thereby lying on top of each other at every point.
An example given in Figure A1 illustrates this by showing a line with a y-intercept of 9 and a slope of 3, where the slope is consistent throughout. Both the slope (m) and the y-intercept (b) are crucial for defining a line's characteristics in the context of a straight line equation.
To address the practice test question, all given equations (A, B, and C) are linear because they can be rewritten in the form y = mx + b, which represents a straight line, where 'm' is the slope and 'b' is the y-intercept.