Final answer:
To graph the inequality –3x – 4y < -6, plot the corresponding line 3x + 4y = -6 on a graph using intercepts, make the line dashed, and then shade the region below the line after determining the correct side with a test point.
Step-by-step explanation:
To solve the inequality –3x – 4y < -6 using the graphing method, start by graphing the line 3x + 4y = -6. First, you'll want to find two points that satisfy the equation of this line. You could set x to 0 to find the y-intercept, and set y to 0 to find the x-intercept. Plot these points on the graph and then draw the straight line through them. Since this inequality is a 'less than', the line on the graph will be dashed to indicate that points on the line are not solutions to the inequality.
Next, you have to determine which side of the line to shade. You can pick a test point that is not on the line (0,0) is usually a good choice unless it is your intercept). Substitute this point into the inequality. If the result is true, shade the region that contains the test point. If the result is false, shade the opposite side. In this case, since 0 is not a solution, the side below the line will be shaded indicating that the solutions to the inequality are located in this region.