Online Study

Introduction to line online study:

In Euclidean geometry, a line is a straight curve. The general form of a line is represented by a equation

Ax + By + C = 0

The above equation of a line can be written as

y = (-`A/B` )x + (-`C/B` )

Plug - A/B  = m and   - C/B = b in the above equation, it becomes

y = mx + b

The above equation is called as slope intercept form of line equation.

Where, m is the slope and

b is the y-intercept

In online, we can study more about this line equation in detail. The example and practice problems are given below which shows how online will helps for your study.

(Source: Wikipedia)

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Example problems of line online:


The following example problems will helps you  to study about line in online.

Example 1:

Find x-intercept of a line y = 4x + 12

Solution:

Step 1: Given line equation

y = 4x + 12

Step 2: Substitute y = 0 in the equation  y = 4x + 12  to find x-intercept.

0 = 4x + 12

Step 3: Solve the above equation for x

Subtract 12 on both side of the equation to cancel 12 from the right hand side of the equation,

-12 = 4x

Multiplying by 4 on both side, we get

- 3 = x

Therefore,

x = - 3

Step 4: Solution

The x-intercept of the given line is (-3, 0)

The following example problems will helps you  to study about line in online.

Example 2:

Find y-intercept of a line 3y = 4x + 12

Solution:

Step 1: Given line equation

3y = 4x + 12

Step 2: Substitute x = 0 in the given equation to find y-intercept.

3y = 4(0) + 12

Step 3: Solve the above equation for y

3y = 0 + 12

Multiplying by 3 on both side, we get

y = 4

Step 4: Solution

The x-intercept of the given line is (0, 4)

Example 3:

Write the following line equation x + 5y = 6 into slope intercept form.

Solution:

Step 1: Given line equation

x + 5y = 6

Step 2: Subtract x on both sides to cancel x from the left hand side of the equation

5y = 6 - x

Step 3: Multiply by 5 on both sides, we get

y = `6/5` - `x/5`

On rearranging, we get

y = - `1/5` x + `6/5`

Step 4: Solution

The slope intercept form of given line equation is y = - `1/5 ` x+ `6/5`

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Practice problems of line online:


1) Find x-intercept of a line y = 8x - 7

2) Find y-intercept of a line 5y = 6x + 15

3) Write the following line equation - x + y = 8 into slope intercept form.

Solution:

1) (7/8, 0)

2) (0, 3)

3) x + 8