Shortcut to finding intercepts

Hello, the math nerd is back! lol. i know sorry, same topic. but this time, i have something cooler. I have a shortcut method to find the x and y intercepts!


General form of the equation of a line: y = mx + b

Here is the shortcut formula for finding the y intercept:  y = b.

meaning: x = 0, y = b.     Point: (0, b)

Proof:

y = mx + b. at the y intercept, x is 0. Let's sub that in.

y = m (0) + b
y = 0 + b
y = b

If there is a constant, a, infront of y, then the shortcut formula would be this: y = b/a.

Proof:
ay = mx + b
ay = m (0) + b
ay = 0 + b
ay = b
y = b/a

Your point would be (0, b/a).

X intercept: shortcut formula is X = -b/m

X = -b/m, y = 0  P: (-b/m, 0)

Proof:

y = mx + b. At the X intercept, y = 0. Sub it in.

0 = mx + b
-b = mx
-b/m = x
x = -b/m

This stays true even if there is a constant before y, since anything multiplied by 0 is still 0.

example: 2y = mx + b

2 (0) = mx + b
0 = mx + b
-b = mx
-b/m = x
x = -b/m


=)