Question

1. locate and label each set of points on the coordinate plane. describe similarities of the ordered pairs in each set, and describe the points on the plane.

a. {(-2, 5) (-2, 2) (-2, 7) (-2, -3) (-2, -0.8)}
b. {(-9, 9) (-4, 4) (-2, 2) (1, -1) (3, -3) (0, 0)}
c. {(-7, -8) (5, -8) (0, -8) (10, -8) (-3, -8)}

Explanation:

Part a: Analyze Ordered Pairs

For the set \(\{(-2, 5), (-2, 2), (-2, 7), (-2, -3), (-2, -0.8)\}\), observe the \(x\)-coordinate of each ordered pair. The \(x\)-value is \(-2\) for all points. In a coordinate plane, points with the same \(x\)-coordinate lie on a vertical line. The equation of a vertical line is \(x = a\) (where \(a\) is the constant \(x\)-coordinate). So, this set of points lies on the vertical line \(x=-2\).

Part b: Analyze Ordered Pairs

For the set \(\{(-9, 9), (-4, 4), (-2, 2), (1, -1), (3, -3), (0, 0)\}\), let's check the relationship between the \(x\)-coordinate (\(x\)) and \(y\)-coordinate (\(y\)) of each ordered pair. For \((-9, 9)\), \(y=-x\) (since \(9=-(-9)\)); for \((-4, 4)\), \(y = -x\) (since \(4=-(-4)\)); for \((-2, 2)\), \(y=-x\) (since \(2=-(-2)\)); for \((1, -1)\), \(y=-x\) (since \(-1=-1\)); for \((3, -3)\), \(y=-x\) (since \(-3=-3\)); for \((0, 0)\), \(y=-x\) (since \(0 = - 0\)). So, all points satisfy the equation \(y=-x\), which represents a line with a slope of \(- 1\) passing through the origin.

Part c: Analyze Ordered Pairs

For the set \(\{(-7, -8), (5, -8), (0, -8), (10, -8), (-3, -8)\}\), observe the \(y\)-coordinate of each ordered pair. The \(y\)-value is \(-8\) for all points. In a coordinate plane, points with the same \(y\)-coordinate lie on a horizontal line. The equation of a horizontal line is \(y = b\) (where \(b\) is the constant \(y\)-coordinate). So, this set of points lies on the horizontal line \(y=-8\).

Graphing (Brief Description)

• For part a: On the coordinate plane, find the vertical line \(x = - 2\) (2 units to the left of the \(y\)-axis) and plot the points \((-2,5)\) (2 units left, 5 up), \((-2,2)\) (2 left, 2 up), \((-2,7)\) (2 left, 7 up), \((-2,-3)\) (2 left, 3 down), \((-2,-0.8)\) (2 left, slightly down from 0).
• For part b: For each point \((x,y)\) where \(y=-x\), plot \((-9,9)\) (9 left, 9 up), \((-4,4)\) (4 left, 4 up), \((-2,2)\) (2 left, 2 up), \((1,-1)\) (1 right, 1 down), \((3,-3)\) (3 right, 3 down), \((0,0)\) (origin). These points lie on the line \(y = -x\).
• For part c: Find the horizontal line \(y=-8\) (8 units down from the \(x\)-axis) and plot the points \((-7,-8)\) (7 left, 8 down), \((5,-8)\) (5 right, 8 down), \((0,-8)\) (origin, 8 down), \((10,-8)\) (10 right, 8 down), \((-3,-8)\) (3 left, 8 down).

Answer:

• Part a: All ordered pairs have \(x = - 2\). The points lie on the vertical line \(x=-2\).
• Part b: All ordered pairs satisfy \(y=-x\) (i.e., \(y + x=0\)). The points lie on the line \(y=-x\) (a line with slope \(-1\) through the origin).
• Part c: All ordered pairs have \(y=-8\). The points lie on the horizontal line \(y = - 8\).

(For graphing: Plot the points as described above on the given coordinate plane.)