To plot inequalities, we need to assume that they have an equal sign and solve for its x and y-intercept.
Let's start with the first inequality.
y < 3x - 1
At x = 0, y = -1 (y-intercept)
y = 3x - 1
y = 3(0) - 1
y = -1
At y = 0, x = 1/3 (x - intercept)
y = 3x - 1
0 = 3x - 1
3x = 1
x = 1/3
Since the x-intercept is 1/3, we will have a hard time plotting it in the graph. So, let's use another possible point.
At y = 2, x = 1 (1, 2) Another possible point in the first inequality.
y = 3x - 1
2 = 3x - 1
2 + 1 = 3x
3 = 3x
x = 1
Let's move on to the next inequality y ≤ x+3.
At x = 0, y = 3 (y-intercept)
y = x + 3
y = 0 + 3
y = 3
At y = 0, x = -3 (x-intercept)
y = x + 3
0 = x + 3
x = -3
Let's plot these points in the graph.
The red one is the graph of the second inequality. It uses a solid line because the inequality is less than or equal to.
The blue one is the graph of the first inequality. It uses a dotted line because the inequality is less than.
Both shaded areas are below the line because the inequality is both less than.
Using the graph in the question, it looks like this however, please make sure that the areas below the lines are shaded just like the previous graph.