Slope from (1, 5) to (3, 1)
Calculate the slope of the line passing through points (1, 5) and (3, 1).
Answer:
Slope m = m = -2
Step-by-Step Solution
Step 1
Slope Formula
The slope of a line through two points is:
m = (y₂ - y₁)/(x₂ - x₁)
This represents 'rise over run' or the rate of change
m = (y₂ - y₁)/(x₂ - x₁)
Step 2
Identify the Points
Point 1: (x₁, y₁) = (1, 5)
Point 2: (x₂, y₂) = (3, 1)
P₁(1, 5), P₂(3, 1)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 1 - 5 = -4
Run = x₂ - x₁ = 3 - 1 = 2
Rise = -4, Run = 2
Step 4
Calculate Slope
m = rise/run = -4/2
m = -2
Step 5
Interpretation
Negative slope: line falls from left to right
For every 2 units of horizontal change, there is 4 units of vertical change
Angle with x-axis: -63.43°
Slope = -2
Step 6
Related Information
Parallel lines have equal slopes: m = -2
Perpendicular lines have negative reciprocal slopes: m = 1/2
Parallel: -2, Perpendicular: 1/2