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?
Try this site https://weteachscience.org/mentoring...ng-slope-and-y

The y-intercept is value for the equation when x = 0. The '2x' term = 0, leaving y=2. For any linear equation , 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 . Here the slope is 5 and the y-intercept is 3 (again, consider how if x=0 then y = 3).

Quote:

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Originally Posted by ebaines

The y-intercept is value for the equation when x = 0. The '2x' term = 0, leaving y=2. For any linear equation , 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 . Here the slope is 5 and the y-intercept is 3 (again, consider how if x=0 then y = 3).

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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: [ and . Plug those into the equation y = mx+b and we get:




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 =

Quote:

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Originally Posted by ebaines

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: [ and . Plug those into the equation y = mx+b and we get:




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 =

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