Write an equation in the form y=mx+b that represents the x-y table

Choose two coordinates. I will choose the ones you chose, (-2, -3) and (0, 1).

Find the slope first using the slope equation:

y2 is 1, y1 is -3, x2 is 0, and x1 is -2.

m =

The slope is 2.

Now that we found out the slope, we can start to assemble our equation. The m in the equation y = mx + b stands for the slope.

Now the equation is: y = 2x + b.

We need to figure out the y-intercept next. The b in the equation stands for the y-intercept. Choose one coordinate. I will chose (0, 1). x = 0 and y = 1. Substitute 0 in for x and 1 into y.

y = 2x + b

1 = 2(0) + b

1 = 0 + b

1 = b

Now we know what b is. Plug in 1 for b in the equation.

y = 2x + 1

I hope this helps! Let me know if I got something wrong and I'll fix it.

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}

square root

step-by-step explanation: