Final answer:
The graph of the linear equation y = 4x - 3 is a solid line which does not pass through the origin, includes the point (2,5), and has a positive slope. It is not dotted, and there is no shaded region since this is not an inequality.
Step-by-step explanation:
The given inequality is y = 4x - 3. When graphing a linear equation such as this, where y is equal to an expression in x, the graph of the solution set is a single line. Here are some details about the graph:
- The graph line is solid because the equation uses an equals sign, indicating that all points on the line are part of the solution set.
- The graph line is not dotted; dotted lines are used for inequalities that do not include the boundary line itself, which is not the case here.
- The graph line does not pass through the origin. The y-intercept is -3, which can be seen from the equation 4x - 3 where y is 0 when x is 0, resulting in the y-intercept (0, -3).
- The ordered pair (2,5) is part of the solution set. This can be verified by substituting x with 2 in the equation to get y = 4(2) - 3 which equals 5.
- The shaded region of the graph representing the solution set would not be to the right or left of the graph line because this is not an inequality but a linear equation. Therefore, there is no shading involved in this graph.
The straight line has a positive slope indicated by the positive coefficient of x, which is 4.