Question

The graph below is represented by which system of inequalities?

Two lines intersecting on a coordinate plane. The first line is a solid line that passes through (-3, 2) and (0, 3) and is shaded below the line. The second line is a dashed line that passes through the points (-1, 3) and (0, 1) and is shaded above the line.

-x + 3y < 9
y > -2x + 1

-x + 3y less than or greater to 9
y > -2x + 1

-x + 3y < 9
y greater than or equal to -2x + 1

None of these systems represent the graph shown.

Answer 1

is it the last one

Answer 2

@JakeV8 @tcarroll010 They need help. I was hoping one of you could take a look at this and see if you could help? Thanks! :)

Answer 3

can anyone help

Answer 4

you need to find the inequalities based on the pairs of points. I normally put them into a form like the y = mx + b line equation (but as an inequality) form first... but this problem makes you put them into a standard form instead.

Answer 5

what is the substitution meathod

Answer 6

I don't know what you would do with substitution method here.

Answer 7

The first line is a solid line that passes through (-3, 2) and (0, 3) and is shaded below the line.

So the slope is (y2 - y1) / (x2 - x1) = (3 - 2) / (0 - (-3) ) = 1 / 3

And the y intercept is given as (0,3), or just "3"...

So the line equation in y = mx + b format is:

y = (1/3)x + 3 and since it's "shaded below the line", it is an inequality like:

y < (1/3)x + 3

Answer 8

what

Answer 9

is it

Answer 10

Well, that's one of the inequalities. Looking at your answer choices, I don't see any "1/3" stuff. But if you multiply the whole thing through by 3, the fraction goes away...

y < (1/3)x + 3

Multiply by 3:
3y < x + 9

That looks more like something in your options, but they show it with x on the same side as y...

-x + 3y < 9

This matches choices 1 and 3.

Answer 11

I haven't worked the other one yet, but it's the same idea... find the slope between the points, find the line equation, and make it an inequality. I'm pretty certain it will match either answer 1 or 3.

Answer 12

The second line is a dashed line that passes through the points (-1, 3) and (0, 1) and is shaded above the line.

So, if you didn't even want to solve this line equation, you might notice also that "shaded above the line" means a "greater than" symbol... not a "greater than or equal to".

That means answer 3 can't work.