3-5 & 3-6 Lines in the Coordinate Plane & Slopes of Parallel and Perpendicular Lines
OBJECTIVES To graph lines given their equations To write equations of lines To relate slope to parallel and perpendicular lines
Equations of Lines Slope-Intercept Form y = mx + b m = slope b = y-intercept (x,y) is any point on that line Standard Form of a Line Ax + By = C Step 1: Find y-intercept, substitute 0 for x; solve for y Step 2: Find x-intercept, substitute 0 for y; solve for x Step 3: Plot two intercepts and draw the line As an alternative, you can transform standard form into slope-intercept form. Point-Slope Form- used to find the equation of a line given a point and the slope y-y1 = m(x-x1) m = slope (x1.y1) is a specific point on the line Slope- m = y2 – y1/x2 – x1 Rise/run Change in y/change in x
Slopes of Parallel Lines If two nonvertical lines are parallel, their slopes are equal If the slopes of two distinct nonvertical lines are equal, the lines are parallel Any two vertical lines are parallel
Slopes of Perpendicular Lines If two nonvertical lines are perpendicular, the product of their slopes is -1 If the slopes of two lines have a product of -1, the lines are perpendicular Any horizontal line and vertical line are perpendicular