Question

Which of the following inequalities matches the graph of a solid line through the points (0,1) and (2, -3) with shading above the line?
a. y ≥ -2x + 1
b. y > -2x + 1
c. y ≤ -2x + 1

Answer 1

so what do you think is the slope of the line that passes through -> (0,1) and (2, -3) ?

Answer 2

slope is -2/1?

Answer 3

hmm, wait a second, I notice all right sides are the same, nevermind the slope then

Answer 4

yes is -2, but all have -2 so

well, anyhow a SOLID LINE in inequality graphing means "y is GREATER THAN" or "y is LESS THAN"

Answer 5

as opposed to GREATER THAN OR EQUALS TO, which means a "dashed line"

Answer 6

oh I missed choice d. The correct inequality is not listed. That's what I think the answer is

Answer 7

so, what's D?

Answer 8

because since it's a SOLID line, you can pretty much rule out A and B

Answer 9

I mean A and C

Answer 10

d. The correct inequality is not listed.

Answer 11

ohh that's D: not listed, darn didn't read correctly heheh

Answer 12

well, ruling out A and C only leaves B

since all A B and C are using the same form for the right-side, then I'd gather that's the equation, and so the choice will be the obvious one

Answer 13

choice d?

Answer 14

h..... wait... darn I got mixed

Answer 15

hold the mayo, a solid line means \(\bf \ge\) or \(\bf \le\)

Answer 16

so is either A or C, man dohhh

Answer 17

Ack! I hate these things!

Answer 18

my bad, that was my mix up though

Answer 19

lemme get the line

Answer 20

there, as you can see, is a declining function, a negative slope -2

so now let's test around some points NOT IN THE LINE

say let's test for say (-2, 1) is not the line

let's plug those values in A)

1 ≥ -2(-2) + 1
1 ≥ 5

so we know that \(\bf 1 \cancel{ \ge } 5\)
so it's not A

Answer 21

now let's test C, our other candidate

same point
(-2, 1) not in the line

1 ≤ -2(-2) + 1
1 ≤ 5

so we do know that indeed \(\large \bf 1 \le 5\)

Answer 22

so, that's your choice

Answer 23

sorry on the mix up
solid lines mean GREATER/LESS OR EQUAL

dashed lines mean GREATER/LESS

Answer 24

wow thanks!!

Answer 25

yw