ANSWER
EXPLANATION
We want to graph the inequality:
[tex]3y - 5x \: < \: - 6[/tex]
To this inequality, we must first of all graph the corresponding linear equation:
[tex]3y - 5x = - 6[/tex]
When x=0, we have
[tex]3y - 5(0) = - 6[/tex]
[tex]3y = - 6[/tex]
y=-2
We plot the point (0,-2)
When y=0,
[tex]3(0) - 5x = - 6[/tex]
[tex]x = \frac{6}{5} [/tex]
[tex]( \frac{6}{5} ,0)[/tex]
We plot the points and draw a dashed straight line through them.
We test for (0,0).
[tex]3(0)- 5(0)\: < \: - 6[/tex]
[tex]0 < \: - 6[/tex]
This is false hence we shade the lower half plane. See attachment.
