Slope from (1, 1) to (4, 7)
Calculate the slope of the line passing through points (1, 1) and (4, 7).
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, 1)
Point 2: (x₂, y₂) = (4, 7)
P₁(1, 1), P₂(4, 7)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 7 - 1 = 6
Run = x₂ - x₁ = 4 - 1 = 3
Rise = 6, Run = 3
Step 4
Calculate Slope
m = rise/run = 6/3
m = 2
Step 5
Interpretation
Positive slope: line rises from left to right
For every 3 units of horizontal change, there is 6 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