Question

Find the slope and y-intercept of each line:

a. (x+2)(x+3)=(x-2)(x-3)+y
b. x=my+b

Please show workings, and I won't accept nonsense answers! Don't answer the question if you don't know what it means!!​

Answer 1

See below

Explanation:

Part A:

`(x+2)(x+3) = (x+2)(x-3) + y`

Resolving Parenthesis

`x^2+3x+2x+6=x^2-3x-2x+6+y\\x^2+5x+6 = x^2-5x+6+y`

Subtracting
`x^2` and 6 to both sides

`5x= -5x+y`

Adding 5x to both sides

`y = 5x+5x\\y = 10x`

Comparing it with
`y = mx+b` where m is the slope while b is the y-intercept

So,

Slope = m = 10

Y-intercept = b = 0

Part B:

`x = my+b`

Subtracting b to both sides

`my = x-b`

Dividing both sides by m

`y = (x-b)/(m)\\ y = (x)/(m) - (b)/(m)`

Comparing it with
`y = mx+b` where m is the slope while b is the y-intercept

So,

Slope = m =
`(1)/(m)`

Y-intercept = b =
`-(b)/(m)`