Horizontal Line

Horizontal Line is found in many shapes such as Rectangle, Square, Hexagon, etc. A horizontal line is a very important part of such figures because, without such horizontal lines, we cannot even think about drawing these shapes. There is another type of line called the Vertical Line. This line extends from the top to the bottom of a plane. If in a plane, there is a vertical line and there is a horizontal line and both these lines intersect, they will be perpendicular to each other.

Horizontal Line Diagram

The above-given figure is the pictorial description of what a Horizontal Line looks like.

Line vs Line Segment

A line can be described as a group of points that extend infinitely in both directions. This statement means that a line does not have any endpoints.

A line Segment can be defined as a line that has endpoints and which does not extend infinitely.

Now we will see figures pertaining to both the Line and the Line Segment to help us better understand the difference.

This is the figure pertaining to a simple horizontal line.

While this is the figure pertaining to a Line Segment.

Parallel Lines

Parallel Lines are described as Horizontal or Vertical Lines in the same plane that are always some distance apart from each other.

Now we will see a figure that will help us better understand parallel lines.

The lines in the above figure are horizontal parallel lines.

The lines in this figure are vertical parallel lines.

Slope of a Line

Slope of a line may be described as the general steepness of a particular line in the coordinate plane. This is a very simple or very basic definition of the slope of a line.

For determining the slope of the line, we have considered two sets of points (x1,y1) and (x2,y2). Therefore we have considered Δx and Δy which are considered as the change in the x coordinate and the change in the y coordinate respectively.

So,

Δx= x2-x1

Δy=y2-y1

Now we define the slope of the line (m),

m= Δy/ Δx

and m is also equal to tan θ

Because in the figure we can see that,

tan θ= Δy/ Δx

If we have to write this in the form of a statement, we can say that the slope of a line is equal to the tan of the angle that the line makes with the positive x-axis.

Now to calculate the slope of the two points.

So we already know that,

Δx= x2-x1

Δy=y2-y1

and we also know that,

tan θ= Δy/ Δx

So,

m=tan θ= (y2-y1)/(x2-x1)

The slope is a very vital component of a line and it is very important in writing the equation of the line.

The equation of the line is given as,

y=mx+b

where m is the slope of the line and b is the y-intercept.

This equation of the line is called the slope-intercept form.

Now we will solve problems related to the topics we have just discussed.

Examples-

Q. Write the equation of a line in the slope-intercept form whose slope is 6 and y-intercept is 8.

Soln. 

y=mx + b

So substituting the values of m and b in the above equation,

y=6x+8

this can also be written as,

y-6x=8

Q. Write the equation of a line in the slope-intercept form whose slope is 9 and y-intercept is -6.

Soln. 

y=mx+b

y=9x+ (-6)

y=9x-6

9x-y=6

Q. Find the equation of a line which has a slope 4 and which passes through the point (1,4).

Soln.

y=mx+b

y=4x+b

We substituted the value of m in the slope-intercept form,

Now substituting the value of x and y in the equation y=4x+b

y=4x+b

4= (4*1) +b

So,

b=4-4=0

so since we got the value of m and b, now we have to substitute these values in the slope-intercept form,

y=mx+b

y=4x+0

So final equation is y=4x

Q. Find the equation of a line which has a slope of 3 and passes through the point (-2, 0).

Soln.

y=mx+b

Substituting the value of m in the above equation,

y=3x+b

Now we have to find out the value of b,

So we have to substitute the value of x and y in the above equation,

0= (3*(-2)) +b

b=6

so now that we have the values of m and b, we can get the final equation,

y=3x+6

y-3x=6

Conclusion

In the first topic of this chapter, we saw the meta description. We briefly defined the concept of a horizontal line and the line in itself.

Then in the Introduction part, we discussed the importance of a horizontal line. We also discussed another type of line called the Vertical Line. Then we saw a pictorial representation of a horizontal line which helped us to visualize the topic better. After that, we compared and saw the differences between a line and a line segment. Then using figures we saw the concept of parallel lines. After that, we came to a very interesting topic called The Slope. We saw many formulae involving the slope and we also solved quite a few problems on the slope of the line.