Equation of Straight Line
The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the yintercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as pointslope form, slopeintercept form, general form, standard form, etc. A straight line is a twodimensional geometrical entity that extends on both its ends till infinity.
In this article, we will explore the concept of the equation of a straight line. We will try to understand the general equation of a line, straightline formula, the way of finding the equation of a straight line, and discover other interesting aspects of it. Try your hands at solving a few interesting examples and questions for a better understanding of the concept.
1.  What is the Equation of Straight Line? 
2.  Forms of Equation of a Straight Line 
3.  Equation of Straight Line on Graph 
4.  FAQs on Equation of Straight Line 
What is the Equation of Straight Line?
The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, xintercept, and yintercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are pointslope form, slopeintercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line:
Equation of Straight Line Formula
A straight line is a figure formed when two points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) are connected with minimum distance between them, and both the ends extended to infinity. The standard form of a linear equation with variables x and y is:
ax + by = c, where a, b, c are constants and x, y are variables.
Forms of Equation of a Straight Line
Suppose a line l makes an angle of θ with a positive direction of the xaxis. The angle θ is called the inclination of the line and tan θ is called the slope of the line. Note that xaxis has a slope 0. In fact, all lines parallel to the xaxis have a slope of 0. Also, the slope of all the vertical lines including the yaxis is not defined. Now that we know the basic form of the equation of a line, let us go through different forms of equations of a straight line:
Standard Form of Equation of Line
The standard form of a straight line is given by ax + by = c, where a, b, c are real numbers. Let us consider an example to transform the equation y = 2x  1 in the standard form. Subtract 2x from both sides of the equation, we have
y  2x = 2x  1  2x
⇒ y  2x = 1
⇒ 2x  y = 1
So, we obtain the standard form of the equation of the line as 2x  y = 1.
PointSlope Form
The equation of a straight line whose slope is m and which passes through a point (x_{1}, y_{1}) is found using the pointslope form. The equation of the pointslope form is:
y  y_{1} = m (x  x_{1}), where (x, y) is an arbitrary point on the line.
Let us see how to find the pointslope form. We will derive this formula using the equation for the slope of a line. Let us consider a line whose slope is m. Let us assume that (x_{1}, y_{1}) is a known point on the line. Let (x, y) be any other random point on the line whose coordinates are not known. We know that the equation for the slope of a line is:
Slope = Difference in ycoordinates/Difference in xcoordinates
⇒ m = (y  y_{1})/(x  x_{1})
Multiplying both sides by (x  x_{1}),
m (x  x_{1}) = (y  y_{1})
This can be written as,
(y  y_{1}) = m (x  x_{1})
Hence the pointslope form of the equation of a line is proved.
SlopeIntercept Form
Now, suppose a line is given to you with its slope m and its yintercept. Say, a line intersects the yaxis at the point (0, c). Using the pointslope form we have y  c = m (x  0) ⇒ y = mx + c, where c is the yintercept. Similarly, if d is the xintercept, then the slopeintercept form of the equation of the line is y = m(x  d).
Equation of Straight Line on Graph
The graph of a linear equation in one variable x forms a vertical line parallel to the yaxis and the graph of the equation of a straight line in one variable y is a horizontal line parallel to the xaxis The graph of a linear equation in two variables x and y forms a straight line.
Important Notes on Equation of Straight Line

The equation of a straight line is also called a linear equation.

If the product of slopes of two straight lines is 1, then lines are perpendicular to each other.

If two straight lines are parallel to each other, then they have the same slope.

Point Slope Form: (y  y_{1}) = m (x  x_{1})

SlopeIntercept Form: y = mx + c

Standard Form = ax + by = c
Related Topics on Equation of Line
Equation of Straight Line Examples

Example 1: Find the equation of a straight line that passes through the points (1, 3) and (2, 4).
Solution: To determine the equation of the line, we will use the formula pointslope form.
For this, we first need to find the slope of the line.
Slope = (43)/(21) = 1/3
Therefore, the equation of the line passing through (1, 3) and (2, 4) is y  4 = (1/3) (x + 2)
⇒ y  4 = x/3  2/3
⇒ y + x/3 = 4  2/3
⇒ x + 3y = 10
Answer: The required equation is x + 3y = 10.

Example 2: The cost of a notebook is $5 more than twice the cost of a pen. Represent the situation as an equation of a straight line.
Solution: Assume cost of pen = $x and cost of notebook = $y. Then, according to the question, we have
y = 2x + 5 which is the equation of a straight line.
Answer: y = 2x + 5
FAQs on Equation of Straight Line
What is the Equation of Straight Line in Coordinate Geometry?
The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the yintercept.
What is a Straight Line in Math?
A straight line is a twodimensional figure formed when two points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) are connected with minimum distance between them, and both the ends extended to infinity.
What is the Formula for the Equation of a Straight Line?
Generally, we represent the equation of a straight line using the formula: ax + by = c, where x and y are variables.
What is the yintercept Formula?
If a line intersects the yaxis at the point (0, c), then c is the yintercept.
How Do you Find the Slope and Yintercept of an Equation of a Line?
The slope m of a line joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by m = (y  y_{1})/(x  x_{1}). The yintercept can be found using the equation by substituting the value of x as 0 into the equation of the straight line and finding the corresponding value of y.
The yintercept of a straight line ax + by = c is found by substituting the x as 0.
How Do you Graph a SlopeIntercept Equation?
The slopeintercept form is given by y = mx + c. It is plotted on a graph by plotting the yintercept c and then making a straight line passing through (0, c) with slope m.
What is the yintercept in y = 2x?
On comparing y = 2x with the slope intercept form of equation of a straight line y = mx + c, , we have c = 0. Hence, the yintercept in y = 2x is 0.
How Do you Write an Equation for a Vertical and Horizontal Line?
The equation of a horizontal line passing through (a, b) is of the form y = b. The equation of a vertical line passing through (a, b) is of the form x = a.
How To Find the Equation of a Straight Line when Given Two Points?
The equation of a straight line joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by y  y_{1} = (x  x_{1})[(y_{2}  y_{1})/(x_{2}  x_{1})]
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