Question

Find the slope and y-intercept of each line:

Answer 1

Answer:

See below

Step-by-step 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

$y = \frac{x-b}{m}\\ y = \frac{x}{m} - \frac{b}{m}$

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

So,

Slope = m = $\frac{1}{m}$

Y-intercept = b = $-\frac{b}{m}$