Final answer:
To graph the system of equations, plot both lines y = 3x - 3 and y = -1/2x + 4 on the coordinate plane using their y-intercepts and slopes, and then identify the point where they intersect.
Step-by-step explanation:
To graph the system of equations on a coordinate plane, we need to plot the lines represented by each equation and see where they intersect. We'll go through the steps for one of the options provided, specifically option D: y = 3x - 3 and y = -1/2x + 4.
For the first equation, y = 3x - 3, we note that the y-intercept (b term) is -3, and the slope (m term) is 3. This means the line will cross the y-axis at (0, -3) and for every one unit increase in x, y will increase by three units. To plot this, we start at the y-intercept (0, -3) and use the slope to find another point, for example (1, 0). We then draw a straight line through these points.
Applying the same process to the second equation, y = -1/2x + 4, the y-intercept is 4, and the slope is -1/2. This line will cross the y-axis at (0, 4), and for each increase of two units in x, y will decrease by one unit. We can plot this by starting at the y-intercept (0, 4) and moving down one unit and to the right two units to find another point (2, 3), then draw the line.
Once both lines are plotted, their intersection will represent the solution to the system of equations.