Find the equation of the line that is parallel to x=5y-8 and pass through (6, -5) in slope intercept form

y=1/5x-31/5 (or y=0.2x-6.2 in decimals)

Step-by-step explanation:

x=5y-8     (original equation)

x+8=5y (Addition Property of Equality)

1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)

y-y1=m(x-x1)    (point-slope formula)

y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)

y+5=1/5(x-6)

y+5=1/5x-6/5   (Distributive Property of Multiplication)   Note:  5 = 25/5

y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)

y=0.2x-6.2 (This is the same answer, but written with decimals)

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}