Question

Determine the type of boundary line and shading for the graph of the inequality y < 2x + 6

answers :

Dashed line with shading on the side that includes the origin.

Solid line with shading on the side that does not include the origin.

Dashed line with shading on the side that does not include the origin.

Solid line with shading on the side that includes the origin.

Answer 1

that's easy its a solid line because of the sign

Answer 2

thanks.

Answer 3

np

Answer 4

so which is the answer lol?

Answer 5

Dreap3 is incorrect, it is actually a dotted line because of the sign "<" The dotted line indicates that nothing on the line is included, ie its not "less than or equal to." In order to determine if you shade above or below, you just plug in a set of points (x,y) that are not on the line. If you chose (0,0) for example, it is below the line. Then just check if it is true:
Is
0 < 2(0) + 6?
yes, so then you shade blow the line. The first one is your answer.

Answer 6

wait so i thought a line under the the sign is a dashed line??

Answer 7

No, you have them backwards dreap. The sign by itself (< or >) means less than or greater than equally. if you were to use a basic equation like y>x, you'll see that if you plug in (0,0) to this equation, that 0>0 is an incorrect statement, therefore you would not want to include that point (or any point on the line) in the solution. Because of this, we make them a dotted line to signify that the line itself is not part of the solution set. If it were \[y \ge x\] then (0,0) is part of the solution set and we make the solid line.

Answer 8

ohhhhhh