Question

algebra 1b
263a slopes of lines
find the slope of each line.
1)
2)
3)
4)
5)
6)

Explanation:

Problem 1:

Step1: Identify line type

The line is vertical (constant \( x \)-value, changing \( y \)-value). For vertical lines, the slope formula \( m = \frac{\Delta y}{\Delta x} \) has \( \Delta x = 0 \), so slope is undefined.

Step2: Confirm with points

Take two points on the line, e.g., \( (4, 3) \) and \( (4, -1) \). \( \Delta x = 4 - 4 = 0 \), \( \Delta y = -1 - 3 = -4 \). \( m = \frac{-4}{0} \), undefined.

Step1: Choose two points

Let's take \( (-3, 0) \) and \( (0, 2) \) (from the graph).

Step2: Apply slope formula

Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-3)} = \frac{2}{3} \).

Step1: Select two points

Take \( (-2, 0) \) and \( (0, 2) \) (from the graph).

Step2: Calculate slope

\( m = \frac{2 - 0}{0 - (-2)} = \frac{2}{2} = 1 \).

Answer:

Undefined

Problem 2: