The equation of a line describes its geometric properties and can be expressed in different forms. One of the most common forms of a linear equation is
the slope-intercept form
Another common form is the point-slope form
Finally, the standard form of the equation of a line
There are three standard forms of the equation of a line:
Slope-intercept form
y = mx + b,
where m is the slope of the line and,
b is the y-intercept. This form is useful when you know the slope and y-intercept of the line.
Point-slope form
y – y1 = m(x – x1),
where (x1, y1) is a point on the line and
m is the slope of the line.
This form is useful when you know the slope of the line and one point that it passes through.
Standard form
Ax + By = C,
where A, B, and C are constants and
A is non-negative.
This form is useful when you need to compare the coefficients of two or more linear equations, or when you are working with linear programming or other optimization problems.
How To Find the Equation of a Line?
To find the equation of a line given two points, you can use the slope formula:
m = (y2 – y1) / (x2 – x1)
Once you have the slope, you can use either the slope-intercept form or the point-slope form to write the equation of the line.
For example, let’s say we want to find the equation of the line passing through the points (2, 3) and (4, 5):
m = (5 – 3) / (4 – 2) = 1
Using the point-slope form with (2, 3) as our point, we get:
y – 3 = 1(x – 2)
Simplifying this equation gives us the slope-intercept form:
y = x + 1
So the equation of the line passing through the points (2, 3) and (4, 5) is y = x + 1.
Straight Line Formulas
Formula Name
Formula
Slope Formula
m = (y2 – y1) / (x2 – x1)
Point-Slope Formula
y – y1 = m(x – x1)
Slope-Intercept Formula
y = mx + b
Two-Point Formula
y – y1 = (y2 – y1) / (x2 – x1) (x – x1)
Intercept Formula
x/a + y/b = 1
Distance Formula
d =
Equation of a horizontal line
y = a or y=-a
Equation of a vertical line
x=b or x=-b
Real life Examples of Straight Lines
The edges of a piece of paper or a book
The lines on a ruled notebook page
The stripes on a flagpole
The creases on a pair of pants
The dashed lines on a road
The straight sections of a railway track
The lines on a graph paper
The boundary lines on a basketball court or soccer field
