Graph the equation. The graph will divide the coordinate plane into four reqions. Write a system of inequalities that describe each region. Labe the region with these inequalities.
1) y = x - 3
y = 9 - x
I already graphed it,
I only need help on writing the systems of inequalites in each regiopn.
HELP?
the one "tilting" north :
y ≥ x-3 AND y ≥ 9 - x
the one "tilting" west:
y ≤ 9 - x AND y ≥ x - 3
You try the rest.
I don't know how to do these things though.
Is there like a step-by-step process in doing it ??
I D K!
5x+3y>-9
To write a system of inequalities that describes each region created by the graph of the given equations, we need to analyze the properties of the equations.
The given equations are:
1) y = x - 3
2) y = 9 - x
To determine the inequalities in each region, we need to identify where the lines intersect and the relative positions of the lines in relation to each other. Based on the graph you've already created, we can proceed as follows:
Region 1: This region lies above both lines. To describe it, we note that in this region, the y-values are greater than both x-3 and 9-x. We can write the inequalities as:
y > x - 3
y > 9 - x
Region 2: This region lies between the two lines. To describe it, we notice that in this region, the y-values lie between x-3 and 9-x. We can write the inequalities as:
x - 3 < y < 9 - x
Region 3: This region lies below both lines. To describe it, we observe that in this region, the y-values are less than both x-3 and 9-x. We can write the inequalities as:
y < x - 3
y < 9 - x
Region 4: This region lies to the left of both lines. To describe it, we notice that in this region, the x-values are less than both 9-x and x-3. We can write the inequalities as:
x < 9 - y
x < y + 3
By writing a system of inequalities that represents each region, you have now described the boundaries and relationships between the given equations on the coordinate plane.