This document explains the point-slope form of a linear equation, which is used to write equations of lines when the slope and a point on the line are known. It includes examples and solutions for determining the equation based on given slopes and points. The point-slope format does not require the y-intercept, simplifying the writing of linear equations.

1. 5.5 POINT-SLOPE FORM OF
A LINEAR EQUATION
OBJECTIVE:
To use the point-slope form to write an equation of a line.

2. 5.5 POINT-SLOPE FORM OF A LINEAR EQUATION
Linear equations can be written using different formats. In previous sections, we
used the slope-intercept form of a linear equation:
𝒚 = 𝒎𝒙 + 𝒃
A second way to write a linear equation is using the point-slope form of a linear
equation. This format is deducted directly from the formula for the slope, when
two points are given:
𝒎 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
𝒎 𝒙 𝟐 − 𝒙 𝟏 = 𝒚 𝟐 − 𝒚 𝟏 𝐲 − 𝒚 𝟏 = 𝒎 𝒙 − 𝒙 𝟏
Slope Formula Using multiplication as inverse operation Point-Slope Form of a
Linear Equation

3. 5.5 POINT-SLOPE FORM OF A LINEAR EQUATION
Basically, you will know the slope and a given point, but you do not need to
calculate the y-intercept (b), because in this format, it is not necessary to identify
the y-intercept.
Example #1: Determine the equation of line, in point-slope form, knowing that the
slope is – 5 and the line is passing through 𝟖, 𝟔 .
Solution: 𝒚 − 𝒚 𝟏 = 𝒎 𝒙 − 𝒙 𝟏 write the point-slope form
𝒚 − 𝟔 = −𝟓 𝒙 − 𝟖 substitute the given information

4. 5.5 POINT-SLOPE FORM OF A LINEAR EQUATION
Example #2: Write the equation of a line, in point-slope form, when the slope is
𝟐
𝟑
and the line is passing through the point −𝟑, −𝟒 .
Solution: 𝒚 − 𝒚 𝟏 = 𝒎 𝒙 − 𝒙 𝟏 write the point-slope form
𝒚 − −𝟒 =
𝟐
𝟑
𝒙 − (−𝟑) substitute the given information
𝒚 + 𝟒 =
𝟐
𝟑
𝒙 + 𝟒 Simplify the equation

5. 5.5 POINT-SLOPE FORM OF A LINEAR EQUATION
GUIDED PRACTICE: write a linear equation, in point-slope form, with the given
information.
𝟏. 𝒎 = 𝟑, 𝑷 −𝟐, 𝟓 𝟐. 𝒎 = −
𝟒
𝟓
, 𝑷 𝟏, −𝟔 𝟑. 𝒎 =
𝟔
𝟏𝟐
, 𝑷 𝟗, 𝟒