Generating Equation of the Line
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:
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).
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.
Using the equation we can easily identify the equation of the line
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.
Using the formula,
where a & b are x and y intercept respectively.
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