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Writing the Equation of a line; How anyone can learn

Writing the Equation of a Line

To write the equation of a line we need to understand the components of what make up a line as well as the various forms we can write the equation of a line in. In this post we will focus on writing the equation of a line in slope intercept form. However I feel it is important to also note common forms you may write a linear equation.

Here is the summary of the different forms of linear equations
1.) $y=mx+b$ Slope intercept form
2.) $Ax+By=C$ Standard form
3.) (y2-y1)=m(x2-x1) Point Slope Form

To write the equation of a line in slope intercept there are two values we need to know; slope and y-intercept. In the first video I will show you how to write the equation of a line given the slope and y-intercept.

Write the equation of a line given the slope and y-intercept


But what if we have to find the slope and y-intercept. There are two forms of a linear equation we can use. Point slope form or slope intercept form. In this next video I will show you how to use both when we are given the slope but not explicitly the y-intercept.

Write the equation of a line through a point, given the slope


If you are not given either the slope or y-intercept but rather two points that the line goes through then you will first need to determine the slope between the two points and then use one of the two points to help determine the y-intercept

Write the Equation of a line given two points


Sometimes knowing if a line is parallel to another can be very helpful in writing the equation of a line. Since parallel lines never intersect we can determine that the slope of our line we need to write the equation of has to have the exact same slope of the line it is parallel to.

Write the Equation of a line through a point and parallel to another line


If the line must be perpendicular to another line then the slopes will not be the same but opposite reciprocals of one another. For example $3 and -(1/3)$ or $-(2/5) and (5/2)$
Write the Equation of a line through a point and perpendicular to another line

 

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