The slope of a line measures how steep the line is and is calculated using the formula:
Slope (m) = (y₂ – y₁) / (x₂ – x₁)
In this case, we have two points: (3, 4) which we can consider as (x₁, y₁) and (4, 1) which will be (x₂, y₂). So:
- x₁ = 3
- y₁ = 4
- x₂ = 4
- y₂ = 1
Plugging these values into the slope formula:
m = (1 – 4) / (4 – 3)
This simplifies to:
m = (-3) / (1) = -3
Thus, the slope of the line that passes through the points (3, 4) and (4, 1) is -3. This negative slope indicates that the line goes downwards as it moves from left to right.