Slop lecture

Slop lecture

• 1.
  Slope of aLine Slope basically describes the steepness of a line
• 2.
  Concept: What isSlope? - SLOPE - +SLOPE + Steepness Rise Run Change inY Change inX Y=mx + b
• 3.
  Definitions of Slope Slopeis simply the change in the vertical distance over the change in the horizontal distance 1 2 1 2 x x y y x y run rise m slope         The ratio of vertical change to horizontal change. The change iny over the change inx
• 4.
  Concept: Definitions ofSlope • • • The tilt or inclination of a line The ratio of vertical change to horizontal change. The change iny over the change inx
• 5.
  1 2 1 2 x x y y m    The formula aboveis the one which we will use to find the slope of specific lines In order to use that formula we need to know, or be able to find 2 points on the line
• 6.
  If a lineis in the form Ax + By = C, we can use the following formula to find the slope: B A m  
• 7.
  Examples      3 1 6 2 1 5 4 6 6 , 5 , 4 , 1        m m 3 2 5 3 2     m y x
• 8.
  Horizontal lines havea slope of zero while vertical lines have no slope Horizontal y= Vertical x= m = 0 m = no slope
• 9.
  What does theline look like when… • You have positive slope? • You have negative slope? • You have zero slope? • You have NO slope? (Undefined)
• 10.
  Slope = 0 PositiveSlope Negative Slope Negative slope is a downer Undefined Slope Concept: Determining Slope
• 11.
  Determine the slopeof the line. The line is decreasing (slope is negative). 2 -1 r ise r un  2 1  2 Find points on the graph. Use two of them and apply rise over run.
• 12.
  Slope Mountain Ski Resort Positive slope, + work Negative slope, –work Zero slope is zero fun! NO slope. Oh No!!!! Concept: Determining Slope cont. . .
• 13.
  1.First pick twopoints on the line The points need to be where the lines cross so they are integers 2. Then find therise and run 3. Determine if the slope of the line is positive or negative Rise = –2 Run = 3 r un r ise slope  3 2  Concept: Determining Slope cont. . .
• 14.
  Concept: Determining Slopecont. . . 1.First pick two points on the line The points need to be where the lines cross so they are integers 2. Then find therise and run 3. Determine if the slope of the line is positive or negative Rise = 10 Run = 2 r un r ise slope  2 10  5 
• 15.
  Slope= 0 Rise= 0 Run= n Concept: Determining Slope cont. . . Special Lines: Horizontal Lines
• 16.
  The Slope is UNDEFINED Rise=n Run = 0 Concept: Determining Slope cont. . .
• 17.
  Concept: Review slope-intercept form Slope-InterceptForm of the Linear Equation y = mx + b m = slope b = y-intercept Any linear equation which is solved for y is in slope-intercept form.
• 18.
  Find the slopeand y-intercept of the following linear equations: y = 3x + 4 m = 3 b = 4 y = -2x - 1 m = -2 b = -1 y = x – 9 4 m = b = 9 4 -2 1 -2 -1 y = 5x m = 5 b = 0 Concept: Review cont…
• 19.
      1: Make surethe equation is in slope-intercept form ( y = mx +b ) 2: Find the slope and y-intercept 3: Plot the y-intercept 4: Apply the slope (rise/run) to the y-intercept Concept: Graphing Using Slope and y-Intercept
• 20.
  Concept: Graphing withslope-intercept 1. 1. 2. 1. Start by graphing the y-intercept (b = 2) . From the y-intercept, apply “rise over run” using your slope. rise = 1, run = -3 Repeat this again from your new point. Draw a line through your points. 1 -3 Start here 1 -3 y  1 3 x  2 Ex: 2
• 21.
  Concept: Graphing slope-interceptcont… They -intercept is –2, so plot the point (0, –2) where the line crosses the y -axis. The equation is already in slope- intercept form. SOLUTION Graphy = x – 2 3 4 Draw a line through the two points. The slope is , so plot a second point on the line by moving 4 units to the right and 3 units up. This point is (4, 1). 3 4 (4, 1) (0, – 2) (0, – 2) 3 4 (4, 1).