Variation and Problem Solving
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| What way does x and y go on a graph? | x is horizontal and y is vertical
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| which of these points are x and y? (-2,1) | x=-2; y=1
(x,y)
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| how to find coordinates for: f(x)=2x | pick a number for x and plug into the formula to find y.
if x=1, then y=2 [f(1)=2(1)] [(1,2)]
if x=0, then y=0 [f(0)=2(0)] [(0,0)]
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| what is the function notation equation | y=mx+b
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| what is line function notation | f(x)=mx+b
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| what are the parts of y=mx+b | m= slope
b= y intercept
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| how to place "slope 2; y intercept (0,1)" into line function notation equation | f(x)=mx+b
place in 2 for m and 1 for b
f(x)=2x+1
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| point-slope equation | y-y1 = m(x-x1)
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| how to find equation of a line when slope 3; through (3,1) | plug into point slope equation
y-1=3(x-3)
y-1=3x-9
y=3x-8
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| how to find slope | y2-y1
m= ------------
x2-x1
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| how to write the equation of a line without slope (-4,-3) (-8,-2) | find slope
(-2)-(-3)
m= ------------ m=1/-4
(-8)-(-4)
y-(-3)=-1/4(x-(-4))
y+3=-1/4x-1
y= -1/4x-4
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| when two nonvertical lines are parallel... | if they have the same slope and different y intercept
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| how to find the equation of a line that goes through (1,1) and is parallel to y=5x+3 | we know that m=5, since they are parallel.
use point slope equation
y-1=5(x-1)
y-1=5x-5
y=5x-4
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| to find the slope of a new line that is perpendicular... | take the negative reciprocal of slope (m)
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| how to write the equation of the line (-10,8) that is perpendicular to 2y=x-6 | divide 2y=x-6 by 2
y=1/2x-3
take the negative reciprocal of slope
m=-2
put into point slope equation
y-8= -2(x+10)
y-8= -2x-20
y= -2-12x
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| what is standard form | x+y= #
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| write into equation and put into standard form slope 6; (-6,9) | y-9=6(x+6)
y=6x+45
6x-y=-45
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