Question

bukolas teacher told him to draw a heptagon on a coordinate plane and label each side with its slope. help him label sides ag, ab, bc, de, and ef with their slopes.

Explanation:

Step1: Find Coordinates of Points

First, determine the coordinates of points A, G, B, C, D, E, F from the graph. Let's assume the grid has x and y axes (though the x - axis labels are a bit unclear, we can infer from the positions). From the graph:

• \( A=( - 6,10) \) (assuming the x - coordinate of A is - 6, y = 10)
• \( G=( - 7,9) \)
• \( B=( - 5,10) \)
• \( C=( - 4,8) \)
• \( D=( - 4,6) \)
• \( E=( - 5,4) \)
• \( F=( - 7,6) \)

Step2: Calculate Slope of AG

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For \( A=(x_1,y_1)=(-6,10) \) and \( G=(x_2,y_2)=(-7,9) \)
\( m_{AG}=\frac{9 - 10}{-7-( - 6)}=\frac{- 1}{-1}=1 \)

Step3: Calculate Slope of AB

For \( A=(x_1,y_1)=(-6,10) \) and \( B=(x_2,y_2)=(-5,10) \)
\( m_{AB}=\frac{10 - 10}{-5-( - 6)}=\frac{0}{1}=0 \)

Step4: Calculate Slope of BC

For \( B=(x_1,y_1)=(-5,10) \) and \( C=(x_2,y_2)=(-4,8) \)
\( m_{BC}=\frac{8 - 10}{-4-( - 5)}=\frac{-2}{1}=-2 \)

Step5: Calculate Slope of DE

For \( D=(x_1,y_1)=(-4,6) \) and \( E=(x_2,y_2)=(-5,4) \)
\( m_{DE}=\frac{4 - 6}{-5-( - 4)}=\frac{-2}{-1}=2 \)

Step6: Calculate Slope of EF

For \( E=(x_1,y_1)=(-5,4) \) and \( F=(x_2,y_2)=(-7,6) \)
\( m_{EF}=\frac{6 - 4}{-7-( - 5)}=\frac{2}{-2}=-1 \)

Answer:

• Slope of AG: \( 1 \)
• Slope of AB: \( 0 \)
• Slope of BC: \( - 2 \)
• Slope of DE: \( 2 \)
• Slope of EF: \( - 1 \)