Final answer:
The student is asked to complete a table and sketch a graph for the linear equation y = 3x - 5. A table is constructed by plugging in values for x into the equation, resulting in a set of (x,y) pairs that are plotted on a graph to illustrate the linear relationship between x and y.
Step-by-step explanation:
The student's question involves completing a table of values and sketching the graph of a linear equation, which is y = 3x - 5. First, we create a table by choosing values for x and then computing the corresponding y values using the equation. For example, if x=1, then y = 3(1) - 5 = -2. Repeating this process with different x values gives us a set of points that represent the dependence of y on x.
Here's a simple table of values for the equation:
- x = 0, y = 3(0) - 5 = -5 (Point: (0, -5))
- x = 1, y = 3(1) - 5 = -2 (Point: (1, -2))
- x = 2, y = 3(2) - 5 = 1 (Point: (2, 1))
- x = 3, y = 3(3) - 5 = 4 (Point: (3, 4))
After plotting these points on a graph, we can connect them with a straight line to create the graphic representation of the given linear equation. The line demonstrates the constant rate of change in the y values as x increases, illustrating the linear relationship between x and y.