Question

Which of the following is the graph of the inequality y-2<-2(x-1)?

A
B
C
5-
1
(2.1)
(0, -3)
OA. Graph A
OB. Graph B
OC. Graph C
OD. Graph D
5
(2, 1)
(4.-1)
50
(1.2)
X
5
(3,-2)
-5
D
(1,2)
5
(3,-2)

Answer 1

C. Graph C

Explanation:

You want to identify the graph for the inequality y -2 < -2(x -1).

Point-slope form

The point-slope equation of a line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

If you compare the boundary line equation for the inequality to this form, you see that ...

k = 2

m = -2

h = 1

This means the boundary line for the graph will be a line with slope -2 through the point (1, 2). Graphs C and D have this boundary line.

Shading

If you consider a variable with a positive coefficient (y) and the inequality symbol (<) and their relationship ...

y < ( )

you see that the solution set is values of y that are less than (below) those on the boundary line. Graph C has shading below the line, so Graph C is the appropriate one for this inequality.

<95141404393>