Sections 2.4 & 2.5 - Lines and Linear Equations in Two Variables

Section Objectives

  1. Find and apply the slope-intercept form of the equation of a line.
  2. Apply the point-slope form of the equation of a line.
  3. Graph a line using its slope and a point.
  4. Find lines parallel or perpendicular to given lines.
  5. Apply lines and linear equations in real-world applications.

Point-Slope Form

Suppose a line with slope passes through the point . Then for any other point on the line, it must be true that

or .

If we think of as a variable point on the line, then these expressions give us equations of the line. The equation in the form is called point-slope form.


Slope-Intercept Form

In the last example, you may have noticed something interesting. When a linear equation is written in the form , we can immediately read off the slope and -intercept. An equation in the form is called slope-intercept form.