Question

Which of the following inequalities matches the graph?

2x + y < 7

2x - y > 7

2x + y < -7

The correct inequality is not listed

Answer 1

@Owlcoffee

Answer 2

okay, first off, we'll replace the "<" with a "="
how would the ecuations look like?

Answer 3

2x + y = 7

2x - y = 7

2x + y = -7

@Owlcoffee

Answer 4

Good, now solve the three of them for y

Answer 5

y=2x+7

y=2x-7

y=2x+-7

@Owlcoffee

Answer 6

Good, now we have 3 ecuation lines, let's analyze each of them individually.

Answer 7

ok

Answer 8

@Owlcoffee lets go

Answer 9

Is the first one correct?
it has a positive slope and a y-intersection that is positive.

Answer 10

its a negative tho right?

Answer 11

Oh. Wait there, there are ecuations that are incorrectly solved for y.
they should be like this:
y=-2x+7

y=2x-7

y=-2x+-7

Answer 12

where did ypu get negative 2?

Answer 13

you pass the 2x, negative to the other side.
for example, the first ecuation:
2x + y = 7
to solve it for y:
y=-2x+7

Answer 14

but there no negative in the first question?

Answer 15

@Owlcoffee

Answer 16

Now, on the first ecuation we have a negative slope and a positive y-intersection

Answer 17

ok

Answer 18

@Owlcoffee

Answer 19

Do you think it's correct if we analyze for x=0 and y=0?

Answer 20

no @Owlcoffee

Answer 21

When you have a line like that, having the area underneath the line shaded means you have y < ______ That immediately throws out the 2nd option where it says y >. Then you look and see the graph has a negative slope. If we look at slope-intercept form of
y = mx + b, m is the slope. This means if we rearrange the equations above, the one which matches our graph is one that has anegative x. Because m is slope and is the number multiplying x, that being negative gives the negative slope we want. So again, we have two options left
2x + y < 7
2x + y < -7

Rearranged we get:

y < -2x + 7
y < -2x - 7

So both these equations fit the criteria we want, a negative x and y <. Theonly difference between the two is 7 and -7. Well, in the form y = mx + b, the b is the part that is only a number and this is the y-intercept. So the top equation says the y-intercept is 7 and the bottom equation says the y-intercept is -7. If you look at your graph, though, the graph hits the y-axis at a positive value of 7, meaning the top equation of y < -2x _ 7 is the correct one.