Question

Algebra IV world problem, need help?

Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)

Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend. (2 points)

Answer 1

(see below)

Explanation:

Part A
`{(y < 4.5),(y > 3.5):}`

To plot:
`color(white)("XXX")`Draw a horizontal line through the point `y=4.5` on the Y-axis.
`color(white)("XXX")`Draw a horizontal line through the point `y=3.5` on the Y-axis.
`color(white)("XXX")`Shade the region between the two line you just drew.

Part B
Point D has coordinates `(x,color(green)y)=(-2,color(green)4)`
`color(white)("XXX")y < 4.5` when `y=color(green)4` is a valid inequality.
`color(white)("XXX")y > 3.5` when `y=color(green)4` is a valid inequality.
Since both inequality restrictions are valid, point D is a valid solution to the inequalities of Part A.

Similarly for Point E.

Part C
If you graph the area defined by `y < 3x-3` you can determine which points (I assume these are school locations) that Timothy can attend.
`color(white)("XXX")`It might be useful to note the following solutions to the equation
`color(white)("XXX")y=3x-3`
can be used to determine this area.
`color(white)("XXX"){:(ul(x),color(white)("xx"),ul(y)),(0,,-3),(1,,0):}`

From this we can see that the only school Timothy is allowed to attend is F.