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

Section Objectives

Find and apply the slope-intercept form of the equation of a line.

Apply the point-slope form of the equation of a line.

Graph a line using its slope and a point.

Find lines parallel or perpendicular to given lines.

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.

Examples

Find an equation of the line with slope passing through the point .

Find an equation of the line passing through the points and . Write your final answer in standard form.

Find an equation of the line with -intercept and slope .

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.

Examples

Rewrite the standard form equation in slope-intercept form. Then determine the slope and -intercept of the line described by the equation.

A line with -intercept passes through the other point . Find the point-slope form of the equation for the line. Also write the equation is standard form.

A lines passes through the point and is perpendicular to the line described by . Find an equation for the line.

Don't forget about horizontal and vertical lines.... Find an equation of the horizontal line that passes through the -intercept of the line described by .