Final answer:
The equations A, B, and C in the student's materials are all linear equations. They represent straight lines on a graph, where A and C have negative slopes and B has a positive slope. Understanding the graph representation and domain is key to mastering the concepts of linear equations and inequalities.
Step-by-step explanation:
The student is working on linear equations and needs to identify which of the given equations are linear. Linear equations have the general form y = mx + b, where m is the slope and b is the y-intercept. From the provided information, the equations A. y = -3x, B. y = 0.2 +0.74x, and C. y=-9.4 - 2x all fit this form and are therefore linear equations.
Understanding the graph representation of these equations is crucial too. Equation A will result in a straight line with a negative slope, B will have a positive slope, and C will again be a line with a negative slope. These are basic characteristics of linear equations in geometry and algebra. Moreover, a linear equation graph will always be a straight line on the Cartesian plane, which reflects the constant rate of change indicated by the slope.
Solving linear equations involves finding the values of the variables that make the equation true. For inequalities, one determines whether an ordered pair is a solution by checking if it satisfies the inequality when substituted into it. A graph can be used to visually inspect whether a point lies in the solution set of an inequality. The domain of the function, however, refers to the set of all possible input values (usually x-values) for which the function is defined.