3. Parallel and Perpendicular The slope is a number that tells "how steep" the line is and in which direction. So as you can see, parallel lines have the same slopes so if you need the slope of a line parallel to a given line, simply find the slope of the given line and the slope you want for a parallel line will be the same. Perpendicular lines have negative reciprocal slopes so if you need the slope of a line perpendicular to a given line, simply find the slope of the given line, take its reciprocal (flip it over) and make it negative.
4. Let's look at a line and a point not on the line (2, 4) Let's find the equation of a line parallel to y = - x that passes through the point (2, 4) y = - x What is the slope of the first line, y = - x ? This is in slope intercept form so y = mx + b which means the slope is –1. 1 -1 4 Distribute and then solve for y to leave in slope-intercept form. So we know the slope is –1 and it passes through (2, 4). Having the point and the slope, we can use the point-slope formula to find the equation of the line 2
5. What if we wanted perpendicular instead of parallel? (2, 4) Let's find the equation of a line perpendicular to y = - x that passes through the point (2, 4) y = - x The slope of the first line is still –1. 1 2 4 Distribute and then solve for y to leave in slope-intercept form. The slope of a line perpendicular is the negative reciporical so take –1 and "flip" it over and make it negative. So the slope of a perpendicular line is 1 and it passes through (2, 4).
![Equations of lines to Remember Slope-Intercept Form ,[object Object],Point-Slope Form ,[object Object],[object Object],General Form ,[object Object],From Intermediate Algebra](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)