Line is one of the three undefined objects in plane geometry. This time, we will tackle line in coordinate plane. I will provide sample problems and solution to understand deeply how to generate equation of a line out of the given conditions.

**Forms of equation:**

Standard form:

Slope intercept form: where is the slope of the line and is the y-intercept

**Sample Problem 1: Given two points**

Find the equation of the line through (-1,3) and (4,-2).

Solution:

To solve this type of problem we need to look for the slope of the line first

And we select one of the of the given points let’s say

Using the Point-Slope formula,

is the desired equation of the line in standard form.

**Sample Problem 2: Given Slope and y- intercept**

Find the equation of the line with slope 2 and y-intercept of 2.

Solution:

Using the equation we can easily identify the equation of the line

By substitution:

is the required equation in standard form

**Sample Problem 3: Given x and y intercepts**

Find the equation of the line with -2 and 3 as x and y intercepts respectively.

Solution:

Using the formula,

where a & b are x and y intercept respectively.

By substitution,

Practice Problems:

1. Find the equation of the line through (2,1) and whose slope is twice the slope of the line 3x-2y-4=0.

2. Find the equation of the line through (-1,2) with 4 as its x-intercept.

3. Find the equation of the line through (2,3) and (-3,1).

4. Find the equation of the line with 3 and -4 as its x and y intercepts respectively.

5. Find the equation of the line with slope of and x-intercept of 3.

Answer key here