Hey, can someone please explain to me , using this example, "y = 2x + 2" , how the 2 is always somehow equal to the Y intercept? It just seems very random to me, even though it isn't. And when you explain how this was discovered/derived, please don't use fancy schmancy science/math terminology.

If Y = X, what would the slope look like?
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The y-intercept is value for the equation when x = 0. The '2x' term = 0, leaving y=2. For any linear equation y=mx + b, the 'm' terms defines the slope of the line ("rise over run") and 'b' is equal to the value of the y-axis intercept. In your example you have both the value of 'm' = 2 and 'b' = 2, which may be a bit confusing in explaining this. Let's consider a different example, such as y = 5x + 3. Here the slope is 5 and the y-intercept is 3 (again, consider how if x=0 then y = 3).

The y-intercept is value for the equation when x = 0. The '2x' term = 0, leaving y=2. For any linear equation y=mx + b, the 'm' terms defines the slope of the line ("rise over run") and 'b' is equal to the value of the y-axis intercept. In your example you have both the value of 'm' = 2 and 'b' = 2, which may be a bit confusing in explaining this. Let's consider a different example, such as y = 5x + 3. Here the slope is 5 and the y-intercept is 3 (again, consider how if x=0 then y = 3).

I understand all this, I just don't get how m is always equal to the slope and b is always equal to the y intercept

Given y = mx+b, b is always equal to the y intercept, because b is the value of y when x = 0.

m is always slope, because a change of +1 in the value of x yields a change of +m in the value of y. Since slope = rise over run, this results in slope equal to m/1, or m. For a more formal explanation, consider two different values of x: x_1 [ and x_2. Plug those into the equation y = mx+b and we get:

y_1 = m x_1+ b
y_2 = m x_2 + b

where (x1,y1) and (x2, y2) are two different points on the line. The slope of the line is the "rise over run" calculated as the change in the y-value divided by the change in the x-value:

slope = (change in y)/(change in x)

slope = \frac {y_2-y_1}{x_2-x_1} = \frac {(mx_2+b)-(mx_1+b)}{x_2-x_1} = \frac {m(x_2-x_1) + b-b} {x_2-x_1} = m

Given y = mx+b, b is always equal to the y intercept, because b is the value of y when x = 0.

m is always slope, because a change of +1 in the value of x yields a change of +m in the value of y. Since slope = rise over run, this results in slope equal to m/1, or m. For a more formal explanation, consider two different values of x: x_1 [ and x_2. Plug those into the equation y = mx+b and we get:

y_1 = m x_1+ b
y_2 = m x_2 + b

where (x1,y1) and (x2, y2) are two different points on the line. The slope of the line is the "rise over run" calculated as the change in the y-value divided by the change in the x-value:

slope = (change in y)/(change in x)

slope = \frac {y_2-y_1}{x_2-x_1} = \frac {(mx_2+b)-(mx_1+b)}{x_2-x_1} = \frac {m(x_2-x_1) + b-b} {x_2-x_1} = m

Thanks for the explanation, I have a much better understanding now.