Slope from (0, 4) to (4, 0)
Calculate the slope of the line passing through points (0, 4) and (4, 0).
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, 4)
Point 2: (x₂, y₂) = (4, 0)
P₁(0, 4), P₂(4, 0)
Step 3
Calculate Rise and Run
Rise = y₂ - y₁ = 0 - 4 = -4
Run = x₂ - x₁ = 4 - 0 = 4
Rise = -4, Run = 4
Step 4
Calculate Slope
m = rise/run = -4/4
m = -1
Step 5
Interpretation
Negative slope: line falls 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