Slope from (2, 3) to (5, 9)
Calculate the slope of the line passing through points (2, 3) and (5, 9).
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) = (2, 3)
Point 2: (x₂, y₂) = (5, 9)
P₁(2, 3), P₂(5, 9)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 9 - 3 = 6
Run = x₂ - x₁ = 5 - 2 = 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