to graph the inequality:
y < 5/3x - 5
first, we need to graph the line:
y = 5/3x - 5
we can graph it locating two points that pass through the line. For example, when x = 0,
y = 5/3(0) - 5
y = -5
Then, the point (0, -5) is on the line. Taking y = 0,
0 = 5/3x - 5
5 = 5/3x
5*3/5 = x
3 = x
Then, the point (3, 0) is on the line.
To graph the inequality, we need to draw the line that passes through (0,-5) and (3, 0) with a dashed line, because the line is not included as a solution of the inequality
Finally, we need to find a point that satisfies the inequality. Take for example, (0,0),
0 < 5/3(0) - 5
0 < -5
which is not true, then point (0,0) is not a solution. So, after drawing the line, we have to shade the side that not includes (0,0), as follows: