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Slope and y-intercept.   Lines have both slope (m) and a y-intercept (b).  Slope describes the steepness of the line as well as its direction.  Positive.

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Presentation on theme: "Slope and y-intercept.   Lines have both slope (m) and a y-intercept (b).  Slope describes the steepness of the line as well as its direction.  Positive."— Presentation transcript:

1 Slope and y-intercept

2   Lines have both slope (m) and a y-intercept (b).  Slope describes the steepness of the line as well as its direction.  Positive slope means the lines go up toward the right; negative slope means it goes down to the right.  The larger the slope, the steeper the line.  A slope of 5 is a very steep line, while a slope of 1/5 is very flat.  The y-intercept tells you where the line crosses the y- axis. Lines

3  Slope

4   You only get better when you practice, so…..  Find the slope of the line that passes through the points:  1. (4,4) and (6,6)2. (3,7) and (4,8)  m = 1 m = 1  3. (7,-5) and (-4,-4)4. (-6,-1) and (7,-6)  m = -1/11 m = -5/13 Slope

5   Slope tells you how to move and the y-intercept tells you where the line cross the y-axis.  y = mx + b……you have seen this before  m is the slope and b is the y-intercept.  When giving the y-intercept, give the coordinates as an ordered pair. (0,b)  You can use those two things to graph any line.  y = 2x + 3  Slope is 2 and the y-intercept is (0,3). Slope - Intercept

6   Try a couple more…….  1. y = 5x – 62. y = -2x + 3  3. y = -1/3x y = 1/2x - 4 Slope-Intercept

7   Now we will practice writing equations.  Remember you have to have a slope (m) and a y- intercept (b) to write an equation.  Write the equation for the line given the slope and intercept.  1. m = 2 y-intercept (0,5)  2. m = -8 y-intercept (0,4)  3. m = ½ y-intercept (0,-3) Slope-Intercept 1.y = 2x y = -8x y = 1/2x - 3

8   Now for the hard ones……  What happens if you have the slope, but not the y- intercept?  Solve for it!!!  Write the equation of the line that has a slope of 2 and passes through (4,6).  y = mx + b  6 = 2(4) + b  6 = 8 + b  b = -2  y = 2x - 2 Slope-Intercept Plug in the numbers that you know: m = 2, y = 6, x = 4 Solve for b. Rewrite in slope-intercept form.

9   I know, that was tricky so try it again….  m = 4 (-1,2)  2 = 4(-1) + b  2 = -4 + b  b = 6  y = 4x + 6 Slope-Intercept m = -1/2 (4,-6) -6 = -1/2(4) + b -6 = -2 + b b = -4 y = -1/2x - 4


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