The equation of the line is an algebraic form and way to represent a set of points. These points together make the line in a coordinate system. These points are all coordinates of that straight line, and we represent the equation of the line with a degree of one equation in algebra. The equation of the line is also known as a linear equation. There are 3 common types of equations of a line and we can use the equation of a line calculator to find all the forms of the line.
The equation of the line is a single representation of the number of points on the line. The general form of the equation of the line ax + by + c = 0 and any point which satisfies the equation. The equation of a line can be written in various forms and types, and we use the various forms to represent the line’s equation. There can be various situations when we need to apply a different method to find the equation of the line.
A Common Type of Equation:
There are three common types of the line equation. We can use the equation of a line calculator to find the general form of the equation of the line and their corresponding relationship with the given type of equation of the line
- Point Slope Form
- Slope Intercept Form
- Standard Form
Point Slope Form:
The general form of an equation of a line is also known to be as the point-slope form.
y – y1 = m(x – x1)
m=(y2 – y1)/(x2 – x1)
Where
(x1, y1)= are points on the line
“m”= slope of the line
- We do remember that In the point-slope form, we only require only two points ( x1,y1) to determine the equation of a line.
- Consider we have two points of the ( x1,y1) and also the values of the slope “m” of the line.
- We only need to put the values of two points and the point & slope (m) in the equation of a line calculator to find the equation of the line.
- The equation of line a always passes through two points and we can draw a straight line when we are able to find two points in the point-slope form.
It is best to use the line equation calculator to find the general form of the equation of the line.
Slope Intercept Form:
The slope-intercept form is one of the simplest forms of the equation of a line. It only includes the slope of the line “m” and the y-intercept “c” to draw an equation of a line. It is quite convenient to use them to find the slope-intercept form of the equation of the line.
y = mx + c
Where:
“m”= slope of the line
“c” = y-intercept of the equation of the line
When we enter the slope of the line and the y-intercept of the equation of the line in the equation of a line calculator
Standard Form:
We can draw a standard form of the line by finding the coefficient of the coordinated “x” and a Y-intercept of the line. It is quite easy to use the line equation calculator to find the standard form of the equation of the line.
There is a condition to draw a standard form and it is A>0 and the A, B, and C should be integers for drawing a line.
Ax + By = C
We can write the standard form of the equation of the line:
Ax + By + C = 0
Where
A, and B = coefficient of the variables x, y
“C” = Y-intercept of the line
We can find the standard form of the equation of the line by entering the coefficient of “x” and “y” and the Y-intercept of the line in the line equation from two points calculator
Practical example:
We are presenting a practical example of the equation of a line solved by the equation of a line calculator. The equation of a line is represented in all the forms of the equation line. We can find the standard form, slope intercept form, and point-slope form.
A line passes through two points and is perpendicular to each other and having slope “5” and ⅕ respectively.
y = mx + c
y = -1.7778x + 24.56
| Slope (m) | -1.7778 |
| Y – Intercept (b) | 24.56 |
| X – Intercept | 13.81 |
Step 1:
Find the equation of a P = (2 , 21) and Q = (11 , 5).
A line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by
m=(y2−y1)/(x2−x1)
x1 = 2 , y1 = 21, x2 = 11 , y2 = 5
Step 2:
Put the given values into the formula for slope:
m=[(5)−(21)]/[(11)−(2)]=−169=−1.7778
Step 3:
y-intercept is
b=y1−m⋅x1 (or b=y2−m⋅x2,
b = 21 – (-1.7778) ⋅ (2) = 24.56
Step 4:
The equation of the line y=mx+b.
y = -1.7778x + 24.56
Slope-intercept form:
The slope-intercept form is:
y = -1.7778x + 24.56
Here the “-1.7778” is the slope of the line and the 24.56 is the y-intercept of the line.
Point-slope form:
The line in the point-slope form is:
y – (21) = -1.7778 ⋅ ( x – (2))
The line in the point-slope form is:
y – (5) = -1.7778 ⋅ ( x – (11))
General equation of the line:
The general equation of the line is:
-1.7778x – y + 24.56 = 0
Conclusion:
The equation of the line is a simple representation of the numerous points in the same line. We can find the equation of the line in a different form like the standard form, slope intercept point, and point-slope form. Any point on the line actually satisfy the equation of the line. We can’t able to find the equation of the line without finding the slope of the line and the y-intercept of the line when we are solving the slope-intercept form. The equation of a line calculator can be used to find any form of the equation of the line in a matter of seconds.