Question

Please help me, I need to get this now

Answer 1

See attachment.

Explanation:

When graphing inequalities:

• < or > : draw a dashed line.
• ≤ or ≥ : draw a solid line.
• < or ≤ : shade under the line.
• > or ≥ : shade above the line.

Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.

Inequality 1

`y \leq -(3)/(2)x-2`

`\begin{aligned}x=0 \implies y&=-(3)/(2)(0)-2\\y&=-2\end{aligned}`

`\begin{aligned}x=2 \implies y&=-(3)/(2)(2)-2\\y&=-5\end{aligned}`

Plot the points (0, -2) and (2, -5).

Draw a solid straight line through the points.

Shade under the line.

Inequality 2

`y > (1)/(2)x+6`

`\begin{aligned}x=0 \implies y&=(1)/(2)(0)+6\\y&=6\end{aligned}`

`\begin{aligned}x=4 \implies y&=(1)/(2)(4)+6\\y&=8\end{aligned}`

Plot the points (0, 6) and (4, 8).

Draw a dashed straight line through the points.

Shade above the line.

The solution to the two inequalities is the overlap of the shaded parts.

Answer 2

see the attachment for a graph

Explanation:

You seem to want a graph of the inequalities ...

• y ≤ -3/2x -2
• y > 1/2x +6

Boundary lines

The equations of the boundary lines are given by replacing the inequality symbol with an equal sign:

• y = -3/2x -2
• y = 1/2x +6

These are graphed in the usual way. It is often convenient to find the y-intercept, then use the slope to locate other points on the line.

y = -3/2x -2

The y-intercept is (0, -2). The line has a rise/run of -3/2, so goes down 3 units for each 2 to the right. Another point on the line is (2, -5).

y = 1/2x +6

The y-intercept is (0, 6). The line has a rise/run of 1/2, so goes up 1 unit for each 2 to the right. Another point on the line is (2, 7).

Line type

When the "or equal to" symbol (≤ or ≥) is used, the boundary line is solid. When the "or equal to" case is not part of the solution, the boundary line is dashed.

The line with negative slope through (0, -2) is solid; the line with positive slope through (0, 6) is dashed.

Shading

All you need to determine shading is a variable with a positive coefficient, and the inequality symbol.

y ≤ . . . . . tells you shading is below the solid line

y > . . . . . tells you shading is above the dashed line

We notice x has a positive coefficient in the second inequality, so we could determine shading from ...

> x . . . . . tells you shading is left of the line (where x values are less than those on the line)

Of course, you can rearrange the inequality so a variable of interest has a positive coefficient. For example, we could add 3/2x to the first inequality to get ...

3/2x + y ≤ -2

Then, looking at the x-variable, we see ...

x ≤ . . . . . tells you shading is to the left of the line