Billy wants to live in the area defined by y < 3x − 6. explain how you can identify the houses in which billy is interested in living. (2 points)

Check the picture below.

to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line y = 3x − 6.

and then you do a "true" or "false" check.

now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.

so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.

y < 3x - 6

y = 0,  x = 0  thus

0 < 3(0) - 6

0 < -6   <--- now, is that really true? is 0 lesser than -6? not quite, is false.

recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.

because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.

we can run a quick check on that btw, say on point 4,4

y =4,   x = 4  thus

4 < 3(4) - 6

4 < 12 - 6

4 < 8    <---- yeap, is true, 4 is lesser/smaller than 8.

hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike ⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.