Question

1. the coordinates of two points on each line are given. indicate which of the points you chose as the first point and which is the second point.

a(6, 4), b(7, 3), where a is (x1, y1) and b is (x2, y2)
c(1, 3), d(3, 1), where c is (x1, y1) and d is (x2, y2)
find the slopes of $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$.
$overleftrightarrow{ab}:m =$
$overleftrightarrow{cd}:m =$

Explanation:

Step1: Recall slope - formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate slope of \(\overleftrightarrow{AB}\)

For points \(A(6,4)\) and \(B(7,3)\), where \(x_1 = 6,y_1 = 4,x_2=7,y_2 = 3\). Then \(m_{AB}=\frac{3 - 4}{7 - 6}=\frac{-1}{1}=- 1\).

Step3: Calculate slope of \(\overleftrightarrow{CD}\)

For points \(C(1,3)\) and \(D(3,1)\), where \(x_1 = 1,y_1 = 3,x_2 = 3,y_2 = 1\). Then \(m_{CD}=\frac{1 - 3}{3 - 1}=\frac{-2}{2}=-1\).

Answer:

\(\overleftrightarrow{AB}:m=-1\)
\(\overleftrightarrow{CD}:m=-1\)