Question

40.) what is the slope for a line that contains the following points?
a.) (-3,2) & (-3,4)
m = ______
b.) (2,4) & (3,-5)
m = ______
c.) (6,8) & (2,8)
m = ______

Explanation:

Part (a)

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((-3, 2)\) and \((-3, 4)\), let \( (x_1, y_1)=(-3, 2) \) and \( (x_2, y_2)=(-3, 4) \).

Step2: Substitute into formula

Substitute into the slope formula: \( m=\frac{4 - 2}{-3 - (-3)}=\frac{2}{0} \). Division by zero is undefined, so the slope is undefined (vertical line).

Part (b)

Step1: Identify coordinates

Let \((x_1, y_1)=(2, 4)\) and \((x_2, y_2)=(3, -5)\).

Step2: Apply slope formula

Using \( m = \frac{y_2 - y_1}{x_2 - x_1} \), substitute values: \( m=\frac{-5 - 4}{3 - 2}=\frac{-9}{1}=-9 \).

Part (c)

Step1: Define points

Let \((x_1, y_1)=(6, 8)\) and \((x_2, y_2)=(2, 8)\).

Step2: Calculate slope

Using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), substitute: \( m=\frac{8 - 8}{2 - 6}=\frac{0}{-4}=0 \).

Answer:

s:
a) \( m \) is undefined (vertical line)
b) \( m=-9 \)
c) \( m = 0 \) (horizontal line)