Final answer:
To graph the inequality y > -5x + 3, plot the line y = -5x + 3 as a dotted line and shade the area below the line. Label the line with its equation.
Step-by-step explanation:
To graph the inequality y > -5x + 3, first plot the line y = -5x + 3 as a dotted line. This line represents the boundary between the areas that satisfy the inequality and those that do not. Since we have a strict inequality (y >), the line should be dotted to show that points on the line itself are not included in the solution set.
Next, choose a test point that is not on the line. For example, (0,0) is a convenient test point. Substitute the coordinates of the test point into the inequality and check if it is true or false. If it is true, shade the side of the line containing the test point. If it is false, shade the other side of the line. In this case, when we substitute (0,0) into y > -5x + 3, we get 0 > 3, which is false. Therefore, we shade the side of the line not containing the test point.
The resulting graph should have a shaded area below the line y = -5x + 3. Remember to label the line with its equation.