SLOPE Change in y There are four types of slope... Slope Intercept Form The slopes of perpendicular lines are negative reciprocals. Parallel lines have the same slope. Slope-Point Form Positive Slope The type of slope has a positive run and a positive rise You have tested positive for both rise and run. Negative Slope This slope has a positive run and a negative rise. RUN RISE Zero Slope This slope has a positive run and zero rise. Undefined Slope This slope has a zero run and a positive rise. Change in x vertical change horizontal change rise run m= rise run m= AKA Example of Positive Slope: Credit: http://math.tutorvista.com/geometry/slope-of-a-line.html Example of Negative Slope: Credit: http://math.tutorvista.com/geometry/slope-of-a-line.html Example of Zero Slope: Credit: http://www.mathscore.com/math/skills/DetSlope.html Example of Undefined Slope: Credit: http://www.mathscore.com/math/skills/DetSlope.html y=mx+b m is the slope

b is the y-intercept y - y1= m (x - x1) This can be written when the slope and the coordinates of a point on the line are known. point: (x1, y1) slope= m Example: The slope of a line is 4/7, and is passing through point (11, -5).

Written in slope-point form, the equation would be: y1= -5

x1= 11 slope: 4/7 y-y1=m(x-x1) y--5 = 4/7 (x-11) y+5 = 4/7 (x-11) [Credit: I made this one up too.] Example: The slope of a line is -5/6. The y-interecept is 3. Written in slope-interecept form, the equation would be: slope: -5/6

y-int= 3 y=mx+b y = -5/6 + 3 [Credit: I made this up alllll by myself.] *If different points on the same line are used, a different equation is written, but it still makes the same graph! Example: point: (-2,3)

equation: y-3=-4/5(x+2) point: (3,-1)

equation: y+=-4/5(x-3) To transfer from slope-point form into slope-intercept form, solve for y. Example: Slope point form equation:

y-3= 4/5 (x+2) Solve for y:

y-3=4/5(x+2)

y=4/5x + 4/5 (2/1) +3

y=4/5x + 8/5 + 3/1

y=4/5x + 8/5 +15/5

y=4/5x + 23/5 Credit: http://math.about.com/od/function1/ss/Parallel-Perpendicular-or-Neither_2.htm Example: Equations y-5= -3/7 (x-2)

and y= -3/7x + 6

are parallel because they both have a slope of -3/7 Example: A line parallel to y=5x +7

could be y= -1/5x + 7 because 5 and -1/5 are negative reciprocals. Credit: http://math.about.com/od/function1/ss/Parallel-Perpendicular-or-Neither_3.htm Flip the number of the slope and change the sign Maria Yanagisawa

F&P10

Per3

March2013 Unit2:Linear Functions

Mind Map LINEAR FUNCTIONS formula: m= y2-y1 x2-x1 Creates a right angle Credit: http://www.sparknotes.com/math/algebra1/writingequations/section2.rhtml General Form Ax + By + C = 0 *A is a whole number, and B and C are integers.

You can get rid of the fractions by multiplying the numbers. Example: To convert this equation, written in standard form, 2x-3y=12 into general form:

Move the 12 to the left, and do 12-12 on the right.

2x-3y-12=12-12

2x-3y-12=0 Credit: From the Pearson F&P textbook, p. 378 Examples: From slope- intercept form:

y=-2/3x+4

3y=3(-2/3x+4)

3y=3(-2/3x)+3(4)

3y=-2x+12

2x+3y-12=0 From Slope-point Form:

y-1=3/5(x+2)

5(y-1)=5(3/5)(x+2)

5y-5=3(x+2)

5y-5=3x+6

5y=3x+11

3x-5y+11=0 Credit: From Pearson F&P textbook, p.379

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# Linear Functions Mind Map

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