Slope from (0, 0) to (1, 1)
Calculate the slope of the line passing through points (0, 0) and (1, 1).
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) = (0, 0)
Point 2: (x₂, y₂) = (1, 1)
P₁(0, 0), P₂(1, 1)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 1 - 0 = 1
Run = x₂ - x₁ = 1 - 0 = 1
Rise = 1, Run = 1
Step 4
Calculate Slope
m = rise/run = 1/1
m = 1
Step 5
Interpretation
Positive slope: line rises from left to right
For every 1 units of horizontal change, there is 1 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