Parallel and Perpendicular Equations

Definitions

• Parallel Lines- have the same slope.– Since they rise and run at the same levels.– Cross the y-axis at different points though.

• Perpendicular Lines- cross at 90°– They make an exact corner.– You have to “flip-op” the slope of a

perpendicular line to get the new equation.

Steps…

Parallel1. Copy the slope of the

equation given.

2. Using the point-slope form, plug in the ordered pair and the slope to find the equation.

Perpendicular1. “flip-op” the slope in

the equation given.

2. Using the point-slope form, plug in the “flip-op” slope and the ordered pair to find the equation.

Write the slope-intercept form of an equation for the

line that passes through (4, –2) and is parallel to the

graph of

Answer: The equation is

Check You can check your result by graphing both

equations. The lines appear to be parallel.

The graph of passes through (4, –2).

Write the slope-intercept form of an equation for the

line that passes through (2, 3) and is parallel to the

graph of

Answer:

Geometry The height of a trapezoid is measured on a

segment that is perpendicular

to a base. In trapezoid ARTP,

and are bases. Can

be used to measure the

height of the trapezoid? Explain.

Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of

Answer: The equation of the line is

Example 5Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of

Answer:

Example 6Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6).

Answer: The equation of the line is

Example 7Write the slope-intercept form for an equation ofa line perpendicular to the graph of and passes through the x-intercept of that line.

Answer: