name
date
period
retrieval
give the name of a geometric figure that fits the following characteristics:
1. a polygon with five sides
2. a polygon with six sides
3. a polygon with eight congruent sides

given the following table, write equations of the lines described.
4. the line that contains all of the points in the table
x | y
-2 | 5
-1 | 2
0 | -1
1 | -4
2 | -7
5. the line that is parallel to the line given by the table, but has a y-intercept at the point (0, 6).
6. the line that is perpendicular to the line given by the table, that has a y-intercept at the point (0, 6).

Question

name
date
period
retrieval
give the name of a geometric figure that fits the following characteristics:
1. a polygon with five sides
2. a polygon with six sides
3. a polygon with eight congruent sides

given the following table, write equations of the lines described.
4. the line that contains all of the points in the table
x | y
-2 | 5
-1 | 2
0 | -1
1 | -4
2 | -7
5. the line that is parallel to the line given by the table, but has a y-intercept at the point (0, 6).
6. the line that is perpendicular to the line given by the table, that has a y-intercept at the point (0, 6).

Accepted Answer

### Question 1
# Explanation:
A polygon with five sides is defined as a pentagon. By the definition of a pentagon in geometry, it is a closed figure with five straight sides.
# Answer:
Pentagon

### Question 2
# Explanation:
A polygon with six sides is known as a hexagon. The term "hexagon" comes from the Greek words "hex" (meaning six) and "gon" (meaning angle or corner), referring to a six - sided closed figure.
# Answer:
Hexagon

### Question 3
# Explanation:
A polygon with eight congruent (equal - length) sides is an octagon. An octagon is a polygon with eight sides, and when the sides are congruent, it is a regular octagon (though the problem just states eight congruent sides, the general name for an eight - sided polygon is octagon).
# Answer:
Octagon (Regular Octagon if we consider congruent sides, but the basic name is octagon)

### Question 4
# Explanation:
## Step 1: Find the slope ($m$)
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(-2,5)$ and $(x_2,y_2)=(-1,2)$. Then $m=\frac{2 - 5}{-1-(-2)}=\frac{-3}{1}=-3$. We can check with another pair, like $(0, - 1)$ and $(1,-4)$: $m=\frac{-4-(-1)}{1 - 0}=\frac{-3}{1}=-3$.
## Step 2: Find the y - intercept ($b$)
The slope - intercept form of a line is $y = mx + b$. We know that when $x = 0$, $y=-1$ (from the point $(0,-1)$). So substituting $x = 0$, $y=-1$ and $m=-3$ into $y=mx + b$, we get $-1=-3(0)+b$, so $b=-1$.
## Step 3: Write the equation
Using the slope - intercept form $y=mx + b$ with $m=-3$ and $b = - 1$, the equation is $y=-3x-1$.
# Answer:
$y=-3x - 1$

### Question 5
# Explanation:
## Step 1: Recall the property of parallel lines
Parallel lines have the same slope. From question 4, the slope of the line in the table is $m=-3$.
## Step 2: Use the slope - intercept form
The slope - intercept form is $y=mx + b$. We know that the y - intercept $b = 6$ (since the line passes through $(0,6)$) and $m=-3$. Substituting these values into the formula, we get $y=-3x + 6$.
# Answer:
$y=-3x + 6$

### Question 6
# Explanation:
## Step 1: Find the slope of the perpendicular line
The slope of the line in the table is $m=-3$. The slope of a line perpendicular to a line with slope $m$ is the negative reciprocal, so $m_{\perp}=\frac{1}{3}$ (because $m	imes m_{\perp}=-1\Rightarrow - 3	imes m_{\perp}=-1\Rightarrow m_{\perp}=\frac{1}{3}$).
## Step 2: Use the slope - intercept form
The slope - intercept form is $y = m_{\perp}x + b$. We know that the y - intercept $b = 6$ (since the line passes through $(0,6)$) and $m_{\perp}=\frac{1}{3}$. Substituting these values, we get $y=\frac{1}{3}x+6$.
# Answer:
$y=\frac{1}{3}x + 6$

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