# The Point-Slope Form Equation Of A Line

Hi. The topic here is on the point slope form equation of a line. If the slope of a line is known and a point on a that line is known then this point slope form equation of the line can be used to help us obtain the form of the line.

The Point-Slope Form Of The Equation Of A Line

Examples

Practice Problems

The Point-Slope Form Of The Equation Of A Line

The point-slope form of the equation of a line with a point () is of the form:

One may want to consider another version of the above equation. This is the version I was shown and taught back in my high school mathematics course a while back. The equation is:

where is a point on the line given a slope . This version replaces () with and the is added on both sides.

To obtain the form, algebra and the distributive law would be applied to either or .

Here is a visual on how the point and line interact.

Source: http://www.mathsisfun.com/data/images/graph-point-slope-a.gif

Examples

1) Given a point (-1, -5) on the line with a slope of 3. The equation of the line in the form is as follows:

Here we have as 3 with and .

Source: http://quicklatex.com/cache3/0f/ql_dd890d520cafcc7d25b3589a89a3230f_l3.png

2) Suppose that there is a point C and D . What is the equation of the line?

First, we determine the slope of the line.

Now, the point-slope form of the equation of the line can be used. This would help in obtaining the form. You can use either C or D as both points are on the line. I will be using point C .

Source: http://quicklatex.com/cache3/14/ql_e0b28be2a7736425fedb44b58d583e14_l3.png

The equation of the line which passes through points C and D is .

Practice Problems

1) Given a slope of and a point J (-2, 10), what is the equation of the line ( form) which passes through point J?

2) Given a slope of and a point K (7, -1), what is the equation of the line ( form) which passes through point K?

3) What is the equation of a line in the form which passes through and ?