Mathematically, we define a line as a two-dimensional figure without any width. If we need to join two points, we can join them with an infinite number of points. These points together form a line.
We can represent every line with an equation. We can represent every line with a universal equation, whether it is a curved line or a straight line. In this article, we will discuss the equation of a straight line.
A straight line is a line which neither bends or twists. Examples of straight lines are rays of sunlight, beams of a candle, a ruler, etc. All these travel straight or exist straight in nature.
The universal equation of a straight line is given by: ax + by = c. We also represent the line as: y = mx + c. Here, m is the slope of the line, c is the intercept and x and y are the coordinates of the points along which the line must be drawn. This is known as the slope form of representing the equation of a line.
We can represent a line in various forms: slope-intercept form, general form, standard form, point-slope form, etc.
If we want to join two straight lines, then we need a line to join them. For example, suppose the coordinates of these points are P (x, y) and Q (n, m). Then we need a line to join these coordinates of points.
The slope is the angle formed between the line and the particular axis we need to construct the line. In other words, the slope is the inclination between a line with the x or y-axis.
One must note that the slopes of the x and y axes are 0 as they are always straight. Therefore, a line parallel to the x-axis will also have a zero slope, and a line parallel to the y axis will also have a zero slope.
The standard equation of line: ax + by = c
Where a, b and c are real numbers.
Consider an equation of line 4x + 6 = 0. In this equation, a = 4, b = 0 and c = -6. Since we do not have any coefficient of y, therefore, the value of y is zero.
We can find the equation of a line if we know the slope and coordinates of a point.
The point-slope form of the line is given by: y – y1 = m (x – x1).
Here, m is the slope of line
x, and y are the arbitrary points.
x1 and y1 are the coordinates of the point along which we need to draw the line.
Let us consider a line with slope m, and a point with coordinates (x1, y1). We know,
Slope = difference in y coordinates / difference in x coordinates
m = (y – y1) / (x – x1)
Multiply both sides by (x – x1), we have,
m (x – x1) = (y – y1)
We can rewrite the above equation as (y – y1) = m (x – x1), the point-slope form.
The slope-intercept form of a line: y = mx + c
Where m is the slope of the line
c is the intercept along the y axis
We can alternatively rewrite this equation as y = mx – d, where d is the x-intercept.
We can represent a straight line on a graph by knowing the coordinates of the line. By using the equation ax + by = c, we can find multiple points of x and y and construct a line as shown: