Q1. Find the slope of the line joining (1, 2) and (4, 8).
m = (y₂ − y₁)/(x₂ − x₁)
m = (8 − 2)/(4 − 1) = 6/3
m = 2
Straight Lines — Class 11
A line is fixed by a slope and a point. Compute the slope and distance between two points, then learn every form of the line equation.
Slopem = (y₂ − y₁)/(x₂ − x₁) = tan θ, where θ is the angle the line makes with the x-axis.
Forms of a lineSlope-intercept y = mx + c; point-slope y − y₁ = m(x − x₁); two-point and intercept forms.
Distance formulaDistance between (x₁,y₁) and (x₂,y₂) = √[(x₂−x₁)² + (y₂−y₁)²].
Parallel & perpendicularParallel lines have equal slopes; perpendicular lines have m₁·m₂ = −1.
Slope & distance calculator Interactive
Enter two points to get the slope of the line joining them and the distance between them.
Slope m—
Distance—
A vertical line (x₁ = x₂) has an undefined slope; a horizontal line has slope 0.
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Slope | m = (y₂−y₁)/(x₂−x₁) |
| Slope-intercept form | y = mx + c |
| Distance of a point from a line | |ax₁+by₁+c| / √(a²+b²) |
| Perpendicular lines | m₁·m₂ = −1 |
Common mistakes & exam wins
- Parallel lines: equal slopes. Perpendicular lines: product of slopes = −1.
- A vertical line has no defined slope; a horizontal line has slope 0.
- Pick the most convenient form: point-slope if you know a point and the slope.
Frequently asked questions
What is the slope of a line?
m = (y₂ − y₁)/(x₂ − x₁); it equals the tangent of the angle the line makes with the positive x-axis.
What is the condition for two lines to be perpendicular?
The product of their slopes is −1 (m₁·m₂ = −1).
What is the slope-intercept form of a line?
y = mx + c, where m is the slope and c the y-intercept.