What is the Equation of a Line?
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:
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.
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.
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
|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
- The edge of a wall or a building
- The seams on a piece of fabric.
Examples of Straight Lines
- The line y = 2x – 3
- The line y = -4x + 7
- The line y = x
- The line x = 2
- The line y = 5
- The line x = -3
- The line y = -2x + 6
- The line y = 0
- The line x = 0
- The line y = -7