Examples on Line
Example 1: Determine the equation of the line for x-axis and y-axis.
Solution:
The x-axis is represented by the equation y=0, while the y-axis is denoted by x=0.
Example 2: Determine the equation of the line with a slope of 6 passing through the point (9,3).
Solution:
We have the slope m=6 and passing coordinates (x0,y0) = (9,3)
Now, by using
(y-y0) = m(x-x0)
(y-3) = 6 (x-9)
y-3 = 6x-54
6x-y = 51
y = 6x-51
Example 3: Determine the equation of a line when passing through (3,2) and (-4,8).
Solution:
Here, the Line is passing through coordinates (x1, x2) = (3,2) and (y1, y2) = (-4,8)
Now,
y-y1 = {(y2-y1)/(x2-x1)}(x-x1)
y-2 = {(8-2)/(-4-3)}/(x-3)
y-2= {6/-7}/(x-3)
-7y+14 = 6x-18
6x+7y-32=0
Example 4: Determine the y-intercept of a line 2x+5y=20.
Solution:
The given equation is 2x+5y=20
Change this equation in this form
x/a+y/b =1.
Now,
2x+5y = 20
2x/20 + 5y/20 = 1
x/10 + y/4 = 1
Hence, the y-intercept is 4.
Example 5: Determine the equation of a line passing through (1,4) and m=6.
Solution:
We have the slope m=6 and passing coordinates (x0,y0) = (1,4)
Now, by using
(y-y0) = m(x-x0)
y-4 = 6(x-1)
y-4 = 6x-6
y = 6x-2
Lines in Geometry: Definition, Types and Examples
A Line is a one-dimensional geometric figure that exists only in length without width and thickness. A Line comprises a group of points; it extends infinitely in opposite directions or combines with other lines to form various shapes. In a two-dimensional plane, a line is uniquely defined by a pair of points. Points situated on the same line are termed collinear.
In this article, we will discuss the introduction, definition of Line, and its meaning. We will also understand the different types of Lines and various equations related to Lines. We will also solve various examples and provide practice questions for a better understanding of the concept of this article.
Table of Content
- Line in Geometry
- Definition of a Line
- Line Segment
- Ray
- Difference Between Line, Line Segment and Ray
- Types of Lines
- General Equation of Line
- Various Forms of Equation of Line
- Point-Slope form
- Two-Point form
- Slope-Intercept form
- Intercept form
- Examples on Line
- Practice Questions on a Line
- FAQs on Line
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