Question

Which shows the graph of the solution set of 3y – 2x > –18?

Answer 1

graph 3y-2x=-18
hmm, ok, x intercept is at y=0 and x=9 so the point (9,0)
y intercept is at x=0 and y=-6 so (0,-6)

all the graphs hit that

ok, so we have 3y-2x>-18
it is > and not ≥ so it is a dotted line
it is one of the first 2

ok, test points
(0,0)
0>-18?
true
so (0,0) is in it

so it is the 2nd one

Answer 2

Option 2

Explanation:

Given : Inequality
`3y-2x>-18`

To find : Which shows the graph of the solution set of given inequality?

Solution :

First, We find the x and y-intercepts and connect these two dots by extending infinitely from both sides.

For x-intercept put y = 0,

`3(0)-2x=-18`

`x=9`

Point is (9,0)

For y-intercept put x= 0,

`3y-2(0)=-18`

`y=-6`

Point is (0,-6)

Next, we test the inequality by choosing a random data point that does not coincide with any of the data points passed by the line.

Let, we choose the origin (0,0)

`3y-2x>-18`

`3(0) - 2(0) > -18`

`0> -18`

The inequality is true for (0,0).

Thus, the shaded region must include this point.

i.e, All of the region to the left bounded by the line is a solution.

The data points are hollow because they are not part of the solution as the inequality is '>'. If it were ≥, then those points would be solid.

Referring to above points the graph showing inequality is Option 2.

Refer the attached graph below.