Finding the slope of a Line

the Slope of a Line Goes up to the right Up to the right, less steep Horizontal Down to the right, more steep Vertical Goes down to the right

Finding the Slope of a Line Graph the line y = 2x + 1 x y -1 1 -1 1 3

Finding the slope of a Line Rise Run The change in y The change in x y x

Finding the Slope of a Line Find the slope of the line y = 2x + 1 Choose 2 points on the line How much does y change from Point 1 to Point 2? y changes from -1 to 3 (1,3) Point 2 increases 4 +4 Change in y = y = Rise = How much does x change from Point 1 to Point 2? x changes from -1 to 1 (-1,-1) increases 2 +2 Point 1 Change in x = x = Run = Change in y/ y / Rise 4 = = 2 Change in x/ x / Run 2

Finding the Slope of a Line Graph the line y = -2x - 2 x y -1 1 -2 -4

Finding the Slope of a Line Find the slope of the line y = -2x - 1 Choose 2 points on the line How much does y change from Point 1 to Point 2? y changes from 0 to -4 decreases 4 -4 Change in y = y = Rise = How much does x change from Point 1 to Point 2? Point 1 (-1,0) x changes from -1 to 1 increases 2 +2 Change in x = x = Run = Change in y/ y / Rise -4 = = -2 (1,-4) Change in x/ x / Run 2 Point 2

Finding the Slope of a Line Slope is represented by the letter “m” Formula for Finding Slope: Given 2 points (x1, y1) and (x2, y2): m = y2 - y1 x2 - x1

Finding the Slope of a Line Find the slope of the line y = 2x + 1 Choose any two points on the line: (-1,-1) and (1,3) x1 y1 x2 y2 m = y2 - y1 x2 - x1 - -1 4 2 m = 3 = = 2 1 - -1

Finding the Slope of a Line What if I reverse the points? (1,3) and (-1,-1) x1 y1 x2 y2 m = y2 - y1 x2 - x1 - 3 -4 -2 m = -1 = = 2 -1 - 1

Finding the Slope of a Line Find the slope of the line y = 2x + 1 Choose any two points on the line: (-1,0) and (1,-4) x1 y1 x2 y2 m = y2 - y1 x2 - x1 -4 2 m = -4 - = = -2 1 - -1

Finding the Slope of a Line Find the slope of the line that contains the points (3,4) and (6,10) x1 y1 x2 y2 m = y2 - y1 x2 - x1 4 6 3 m = 10 - = = 2 6 - 3

Finding the Slope of a Line Find the slope of the line that contains the points (-5,8) and (-4,-2) x1 y1 x2 y2 m = y2 - y1 x2 - x1 8 -10 1 m = -2 - = = -10 -4 - -5