we have
[tex]y > \frac{3}{4}x-2[/tex]
using a graph tool
see the attached figure
The solution is the shaded area
Statements
A The slope of the line is [tex]-2[/tex].
The statement is False
Because the slope of the line is equal to [tex]\frac{3}{4}[/tex]
B The graph of [tex]y > \frac{3}{4}x-2[/tex] is a dashed line
The statement is True
The graph of the inequality is a dashed line, because it has no equal signs in the problem
C The area below the line is shaded
The statement is False
Because The solution is the area above the dashed line
D One solution to the inequality is [tex](0,0)[/tex]
The statement is True
because
For [tex]x=0[/tex] and [tex]y=0[/tex]
substitute in the inequality
[tex]0 > \frac{3}{4}*0-2[/tex]
[tex]0 > -2[/tex] --------> the inequality is satisfied
E The graph intercepts the y-axis at [tex](0,-2)[/tex]
The statement is True
see the attached figure
