Slope from (1, 2) to (5, 6)
Calculate the slope of the line passing through points (1, 2) and (5, 6).
Answer:
Slope m = m = 1
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, 2)
Point 2: (x₂, y₂) = (5, 6)
P₁(1, 2), P₂(5, 6)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 6 - 2 = 4
Run = x₂ - x₁ = 5 - 1 = 4
Rise = 4, Run = 4
Step 4
Calculate Slope
m = rise/run = 4/4
m = 1
Step 5
Interpretation
Positive slope: line rises from left to right
For every 4 units of horizontal change, there is 4 units of vertical change
Angle with x-axis: 45.00°
Slope = 1
Step 6
Related Information
Parallel lines have equal slopes: m = 1
Perpendicular lines have negative reciprocal slopes: m = -1
Parallel: 1, Perpendicular: -1