Straight Line Formula Overview
We see a lot of items every day that are perfectly straight and aligned along lines that are comparable to our own or that are parallel to other lines that are the same length or different in length but nonetheless straight. This is a scientific idea, but mathematically, every fixed line or curve on the line segment may be described as a straight line. If we add those sides, however, we would be looking at full geometric relations where adding up lines would build up diverse forms.
Also Read: ILATE Rule
What is a Straight Line?
A construction having just a one-dimensional form, no width, and an infinite length can be used to represent a straight line. There appear to be an endless number of points linked between the two specified places in its construction. It appears that the straight-line structure has no bends at all. It is always possible for it to be horizontal, vertical, or inclined. The angle that appears when an angle is placed on a straight line always seems to be 180 degrees.
Example of Straight Line
Railway tracks, measuring tools, and even portions of mirrors can be considered straight lines, to name a few instances of straight lines.
What is the Straight Line Formula?
A straight line's general equation is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most frequent form of a straight-line equation used in geometry. A straight line is a two-dimensional geometrical element that extends indefinitely on both ends.
What is the Equation of a Straight Line?
The equation of a straight line is atwo-variable linear equation that is fulfilled by every point on the line. That is, it is a mathematical equation that expresses the relationship between the coordinate points on that straight line. It may be expressed in several ways and indicates the slope, x-intercept, and y-intercept of a line. It may also be used to find the points on a line. The equation of a straight line is often obtained using point-slope form, slope-intercept form,two-point form, standard form, and so on. The most frequent formulas for determining the equation of a straight line are listed below-
Standard Form
ax + by = c
Slope Intercept-Form
y = mx + c
Point Slope Form
y - y1= m (x - x1)
Equation of Stright Line Formula
The straight line formula equation changes based on the information known about the line, such as slope, intercepts, and so on. The slope of a line with two points (x1, y1) and (x2, y2) may be determined using the formula m = (y2- y1)/(x2- x1). The following table gives details about the examples of straight-line formulae-
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Different Forms of Straight Lines |
Equation of Straight Line |
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Equation of a horizontal line with some point (a, b) on it |
y = b |
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Equation of a vertical line with some point (a, b) on it |
x = a |
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General/Standard Form of a Line |
ax + by = c |
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Intercept Form (Given the intercepts a and b) |
x/a + y/b = 1 |
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Normal Form (Given θ = the angle made by the normal with the positive direction of the x-axis and p = distance of the line from the origin) |
x cos θ + y sin θ = p |
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Point-Slope Form (Given slope m and point (x1, y1)) |
y - y1= m (x - x1) |
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Slope - Intercept Form (Given slope m and y-intercept (0, c)) |
y = mx + c |
|
Two Point-Form (Given two points (x1, y1) and (x2, y2) on the line) |
y - y1= (y2- y1)/(x2- x1) (x - x1) |
Read more about the Maths Formulas.
Forms of Straight Line Formula
A straight line's equation often includes a slope. If a line creates an angle with the positive direction of the x-axis, then the angle is known as the line's inclination, and the slope is known as the line's slope. Take note of thex-axis's slope of 0. In actuality, the slope of all lines parallel to the x-axis is 0. Additionally, the slope of every line parallel to the y-axis, including the y-axis itself, is not known. The following are some of the forms of the straight-line formula-
Point-Slope Form
The point-slope form is used to get the equation of a straight line through the point (x1, y1) with slope m. The point-slope form's equation is-
Where (x, y) is any point on the line, y - y1= m (x - x1).
We are aware of the following equation for a line's slope-
Slope = the difference between y/ x coordinates
⇒ m = (y - y1)/(x - x1)
Multiplying both sides by (x - x1),
m (x - x1) = (y - y1)
This can be written as,
(y - y1) = m (x - x1)
Thus, the proof for the point-slope form of the equation of a straight line.
Two Point Form
A line with the two points (x1, y1) and (x2, y2) on it is an example. The slope's value may then be determined using the formula m = (y2- y1)/(x2 - x1). When this is substituted in the point-slope form mentioned above, the two-point form is obtained as y - y1= (y2- y1)/(x2- x1) (x - x1).
Slope-Intercept Form
Now imagine that you are given a line with the slope m and the y-intercept. Let's say a line crosses the y-axis at (0, c). We may write y - c = m (x - 0) y = mx + c, where c is the y-intercept, using the point-slope form. This is referred to as a line's slope-intercept form.
NOTE: The slope-intercept version of the line's equation is y = m (x - d) if d is the x-intercept.
Intercept Form
If a line's x- and y-intercepts are (a, 0) and (0, b), then, correspondingly. The slope of the line is thus m = (b - 0)/(0 - a) = -b /a. The point-slope form of its equation is thus as follows-
y - 0 = -b/a (x - a)
Multiplying both sides by a,
ay = -bx + ab
bx + ay = ab
Dividing both sides by ab,
x/a + y/b = 1
Standard Form
A straight line's standard form is provided by the equation axe + by = c, where a, b, and c are real values. Any configuration of a line can be considered standard. Let's look at an illustration of how to put the equation y = 2x - 1 in standard form. Add 2x to neither side of the equation, and we get
y - 2x = 2x - 1 - 2x
⇒ y - 2x = -1
⇒ 2x - y = 1
As a result, we arrive at the line's conventional form, which is 2x - y = 1.
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How to Find the Line Equation?
The following are some of the steps to follow to find the line equation-
Step 1: Write down the given information, the line's slope as "m," and the coordinates of the given point or points in the form (xn, yn).
Step 2: Based on the provided parameters, apply the necessary formula.
- The slope-intercept form is used to get the equation of a straight line given its slope or gradient and its intercept on the y-axis.
- Given the slope of a line and the coordinates of a single point that is located on the line-point slope form, one may determine the equation of a straight line.
- Given the coordinates of two points that lie on it, the equation of a straight line may be found using the two-point form.
- Given the x-intercept and y-intercept forms, create an equation.
Step 3: Rearrange the terms to get a standard form equation for the line.
Points to Remember
- A linear equation in two variables is another name for the equation of a straight line.
- Lines are perpendicular to one another if the sum of the slopes of two straight lines equals one.
- (y - y1) = m (x - x1) in point-slope form.
- Form of the Slope-Intercept: y = mx + c
- Formal Formula: axe + by = c
- The slope of two straight lines is the same if they are parallel to one another.