SLOPE SECTION 3-3 Spi.2.1.D Jim Smith JCHS

The Slope Of A Line Is The Ratio Of The Vertical Rise To The Horizontal Run

Let’s move from point A to point B Let’s move from point A to point B. We’ll take the elevator down 9 floors. (down is negative) Then we’ll run right, across the hall 9 spaces. ( right is positive) We end up with the rise = -9 run 9 A SLOPE = -9 = -1 9 -9 B 9

D C Now move from D to C Down 3 (neg) Left 8 (neg) Rise = -3 = 3 Let’s move from C to D. Move up 3. (Up is positive) Move right 8. Rise = 3 Run 8 Now move from D to C Down 3 (neg) Left 8 (neg) Rise = -3 = 3 Run -8 8 8 D 3 -3 C -8

RISE = Y1 – Y2 RUN X1 – X2 Think …”The rise is the Y’s” The slope of a line is the RISE RUN Think …”The rise is the Y’s” RISE = Y1 – Y2 RUN X1 – X2 Y’s on top. It doesn’t matter which Y goes first. Just start with the X from the same pair.

Find The Slope Of The Line Through: (3,6) and (-4,7) 6-7 = -1 =_ 1 3-(-4) 7 7 (4,8) and (9,2) 8-2 = 6 = _ 6 4-9 -5 5 (-3,-7) and (-9,-1) (-7)-(-1) = -6 = -1 (-3)-(-9) 6 (12,9) and (6,0) 9-0 = 9 = 3 12-6 6 2

If You Read A Line From Left To Right And It Goes Uphill, It Has A Positive Slope. Downhill Means A Negative Slope. pos neg

There are 2 special cases. A vertical line has an undefined slope. That means the x’s are equal so we get a 0 in the bottom of our fraction (ex. 5/0). A horizontal line has a slope of zero. The y’s are equal so the 0 is in the top of the ratio ( ex. 0/4). Remember horizontal and zero both have a Z .

¼ and ¼ ½ and -2 Parallel lines Perpendicular lines PARALLEL or PERPENDICULAR Parallel Lines Have The Same Slope. Perpendicular Lines Have Slopes That Are Opposites And Reciprocals Parallel lines Slopes ¼ and ¼ Perpendicular lines Slopes ½ and -2

Are AB and CD parallel, perpendicular or neither? A(-2,-5), B(4,7), C(0,2), D(8,-2) Slope of AB = -5 – 7 -2 – 4 = -12 -6 = 2 Opposites and reciprocals Slope of CD = -2 - 2 8 - 0 = -4 8 _ 1 2 PERPENDICULAR

Are AB and CD parallel, perpendicular or neither? A(4,3), B(5,2), C(0,0), D(5,1) Slope of AB = 3 - 2 4 - 5 = 1 -1 ARE THE SLOPES THE SAME ? OPP and RECIP ? NEITHER Slope of CD = 1 - 0 5 - 0 = 1 5

Graph the line with a slope of 3 and passes Through (2,1) Slope = 3 = 3 1 3 also = -3 -1 (2,1)

-1 4 First find the slope CT Slopes of Perpendicular lines are Graph the line that passes through ( 3,2 ) and is perpendicular to CT with C( 2,2 ) , T( 4,10 ) First find the slope CT Slope of CT = 10-2 8 4-2 2 = = 4 or 4 1 Slopes of Perpendicular lines are opposites and reciprocals Slope of new line = -1 4

Slope -1/4 Passes through ( 3 ,2 )