What is the diference between slope and y-intercept?

Question

SLOPE (m) and Y-INTERCEPT (b) are two essential pieces of information you need to graph a line correctly... but how are they different?

Answer 1

Think of y-intercept as how good you are at something right now. It is a POINT. Let's say I rate my guitar playing as a 40 out of 100. The Y-INTERCEPT is the point (0, 40). The X-COORDINATE of a y-intercept is always 0 because we can think of the X-AXIS as time, so 0 means no time has passed yet. The Y-COORDINATE is whatever I am measuring, in this case my skill level.

The SLOPE is *not* a point- It is a measure of how fast something is changing. So perhaps it takes me a month or practice to raise my skill level to, for example, 55. We could label the x-axis as days, so day 30 and a skill level of 55 would indicate a second point at (30, 55).

How fast did my skill level change? 15 points (the change in what I am measuring) over 30 days (the time it took). 15/30 reduce to 1/2, and that is your slope (which is often more useful when left in fraction form),

Answer 2

Slope is "rise over run", "y inter" is the point on the vertical axis.

Answer 3

y-intercept: the point on the y-axis at which the line crosses (intercepts_

slope: the change in the ordinate (value in the range) divided by the change in the abscissa (value in the domain)