Straight Line Products

Introduction to Straight Line Products:
In geometry, line is one dimensional shape that has no end points.Line is a fundamental concept in the mathematics. Line is representing the straight line object. Geometrical object that is straight, infinitely long is called line. Line is the one dimensional figure. Lines have the no height and  then no width. In this article we see detailed about the straight line products. In this article we are discuss the straight line products.

Example Problems for Straight Line Products:

Straight line products – Example: 1

Find the equation of the straight line passing through the points (1,1),(2,3)

Solution:

The equation of the straight line passing through two points is

`y-y_1=m(x-x_1)` where m is a slope.

`y-1=\frac{3-1}{2-1}(x-1)`

`y-1=2x-2`

`y-2x+1=0`

The equation of the straight line is `y-2x+1=0.`

Straight line products – Example: 2

Find the equation of the straight line passing through (-4,5) and cutting off equal intercepts on the coordinate axes.

Solution:

Let the intercept be a

Now the equation of the line is

`\frac{x}{a}+\frac{y}{a}=1`

`x+y=a`

Since the point (-4,5) passes throough this line,

we get

`a=1`

Hence the equation of the line is

`x+y=1`

Straight line products – Example: 3

Find the equation of the straight line passing through (3,-4)  and making intercepts in the ratio 2:3.

Solution:

Let the intercepts be 2k,3k

Then the equation of the line is

`\frac{x}{2k}+\frac{y}{3k}=1`

`3xk+2yk=6`

Since the line passes through (3,-4)

`9k-8k=6`

Hence the equation is

`\frac{x}{12}+\frac{y}{18}=1`

`3x+2y=36`


Practice Problems for Straight Line Products:

1. Find the equation of the straight line passing through (4,-3)  and perpendicular to the line joining (1,1),(2,3).

`Answer: 2y-x+2=0`

2. Show that the equation of the straight line passing through `(x_1,y_1)` and making an angle of \theta  with the X-axis in positive direction is `\frac{x-x_1}{\cos\theta}=\frac{y-y_1}{\sin \theta}.`

3. Find the equation of the straight line which makes `135^\circ`   with X-axis and passing through (3,-2)

`Answer: y+x-1=0`