Question

fluency

1. for each equation shown below do the following: write down two points that must lie on the line, graph the line on the grid given, and state what type (horizontal or vertical) the line is. label each line with its equation once you plot (draw) it.

(a) ( x = 8 )
points:
type:
(b) ( y = 5 )
points:
type:
(c) ( x = - 2 )
points:
type:
(d) ( y = - 6 )
points:
type:
(e) ( x = 4 )
points:
type:
(f) ( x = - 9 )
points:
type:
(g) ( y = - 3 )
points:
type:

Explanation:

(a) \(x = 8\)

Step1: Find two points

For \(x = 8\), \(y\) can be any value. Let \(y = 0\) and \(y = 1\). Points are \((8,0)\) and \((8,1)\).

Step2: Determine line type

Since \(x\) is fixed (\(x = 8\)), the line is vertical.

(b) \(y = 3\)

Step1: Find two points

For \(y = 3\), \(x\) can be any value. Let \(x = 0\) and \(x = 1\). Points are \((0,3)\) and \((1,3)\).

Step2: Determine line type

Since \(y\) is fixed (\(y = 3\)), the line is horizontal.

(c) \(x=-2\)

Step1: Find two points

For \(x = - 2\), \(y\) can be any value. Let \(y = 0\) and \(y = 1\). Points are \((-2,0)\) and \((-2,1)\).

Step2: Determine line type

Since \(x\) is fixed (\(x=-2\)), the line is vertical.

(d) \(y = - 6\)

Step1: Find two points

For \(y=-6\), \(x\) can be any value. Let \(x = 0\) and \(x = 1\). Points are \((0,-6)\) and \((1,-6)\).

Step2: Determine line type

Since \(y\) is fixed (\(y = - 6\)), the line is horizontal.

(e) \(x = 4\)

Step1: Find two points

For \(x = 4\), \(y\) can be any value. Let \(y = 0\) and \(y = 1\). Points are \((4,0)\) and \((4,1)\).

Step2: Determine line type

Since \(x\) is fixed (\(x = 4\)), the line is vertical.

(f) \(x=-9\)

Step1: Find two points

For \(x=-9\), \(y\) can be any value. Let \(y = 0\) and \(y = 1\). Points are \((-9,0)\) and \((-9,1)\).

Step2: Determine line type

Since \(x\) is fixed (\(x=-9\)), the line is vertical.

(g) \(y=-3\)

Step1: Find two points

For \(y = - 3\), \(x\) can be any value. Let \(x = 0\) and \(x = 1\). Points are \((0,-3)\) and \((1,-3)\).

Step2: Determine line type

Since \(y\) is fixed (\(y=-3\)), the line is horizontal.

Answer:

(a) Points: \((8,0)\), \((8,1)\); Type: Vertical
(b) Points: \((0,3)\), \((1,3)\); Type: Horizontal
(c) Points: \((-2,0)\), \((-2,1)\); Type: Vertical
(d) Points: \((0,-6)\), \((1,-6)\); Type: Horizontal
(e) Points: \((4,0)\), \((4,1)\); Type: Vertical
(f) Points: \((-9,0)\), \((-9,1)\); Type: Vertical
(g) Points: \((0,-3)\), \((1,-3)\); Type: Horizontal