Question

Given the inequality below:
3x-y>4 Which is the graph of the solution set?

Answer 1

`3x-y > 4\ \ \ |-3x\\\\-y > -3x+4\ \ \ \ |change\ signs\\\\y < 3x-4`

`y=3x-4\\\\for\ x=0\to y=3(0)-4=-4\to(0;-4)\\for\ x=2\to y=3(2)-4=6-4=2\to(2;\ 2)`

Answer 2

A shaded region below a dashed line (y <3x-4)

Explanation:

For linear inequalities, we have shaded regions below or above a dashed or solid or continuous line represented by an inequality.

Their graphs are called region graphs. Those regions are only enclosed ones if before the sign of inequality it is included both variables. Like x²+y²<1, |x+y|<1, etc.

In this case what we have here is an open region, as the graph below shows.

3x-y>4 =-y>4-3x∴y<3x-4

Setting a value for x

3x-4=0

3x=4

3x/3=4/3

x=4/3 (slope)

(4/3,0)