Coordinate Geometry

Equation of a Line (Slope-Intercept Form)

Formula

y = mx + c

What is Equation of a Line (Slope-Intercept Form)?

The slope-intercept form of a line gives the relationship between x and y. The coefficient m is the slope, and c is the y-intercept (where the line crosses the y-axis).

Variables

y
y — Dependent variable
m
m — Slope of the line
x
x — Independent variable
c
c — y-intercept

Worked Examples

Example 1

Find the equation of a line with slope 2 and y-intercept 3.

Solution:

y = 2x + 3

Example 2

Find the equation of a line passing through (1, 5) with slope −1.

Solution:

y = −x + c. Substitute (1,5): 5 = −1 + c, so c = 6. Equation: y = −x + 6

Frequently Asked Questions

Related Formulas

Slope of a Line

m = (y₂ − y₁) / (x₂ − x₁)

Distance Between Two Points

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Midpoint Formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

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