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find an equation of the line through (-1,4) and perpendicular to 2x+3y=8

Hello:

2x+3y=8

y =(-2/3)x+8/3  (the slope is : (-2/3) )

 is : y = ax+b
the slope is a : a×(-2/3) = -1( perpendicular to a line with a slope of -2/3)
a = 3/2          y=(3/2)x+b
the line that passes through (-1, 4) :4 = (3/2)(-1)+b
b =11/2
 the equation is :  y  = (3/2)x+11/2

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step-by-step explanation:

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the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.