# Origin of y=mx+b: Explaining Slope & Y-Intercept

• Liger20
In summary, the letters used in the equation y=mx+b for slope and y-intercept have origins in different languages and mathematical conventions. The letter 'm' is thought to come from the French or Latin word for mountain, representing the slope of the line, while 'b' may have originated from the word base or some other term for a low point where the line meets the flat surface. In different countries, different letters may be used to represent these values, such as 'q' in Italy, 'a' in Norway, and 'c' in Britain. The use of 'm' and 'b' in the
Liger20
Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.

"m" comes from "mont", or "mount", or some french or latinized word meaning mountain, or sloping grade. The "b", I'm not sure about. Maybe (just a wild guess) base, bass, some word meaning low point, like where the "mountain" meets the "flat". I'm more certain about the "m" for "mont" as the slope.

Liger20 said:
Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.

The b problably comes from the fact that polynomials are typically written y=ax^n+bx^n-1+cx^n-2 etc. But the special case of a linear polynomial a=m (from what symboipoint said) and the b probably just stayed.

In Italy, they don't use b, they use q.

In norway, m is called a.

And in Britain, 'b' is called 'c'!

Wow, you guys have really strange alphabets!

I always enjoyed $$n \cdot p_0 = n \cdot \left[ \begin{array}{c}x\\y\end{array} \right]$$

## 1. What does the equation y=mx+b mean?

The equation y=mx+b is known as the slope-intercept form of a linear equation. It represents a line on a graph and helps us understand how the value of y changes in relation to the value of x. The letter m represents the slope or steepness of the line, while b represents the y-intercept, which is the point where the line crosses the y-axis.

## 2. How do you find the slope of a line?

The slope of a line can be calculated by dividing the change in y-values (vertical change) by the change in x-values (horizontal change) of any two points on the line. This can also be represented as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line. In the equation y=mx+b, the value of m represents the slope of the line.

## 3. What does the y-intercept represent?

The y-intercept is the point at which the line crosses the y-axis. In the equation y=mx+b, the value of b represents the y-coordinate of the y-intercept. It tells us the starting value of y when x is equal to 0, and helps us understand the position of the line on the y-axis.

## 4. Can the slope and y-intercept have negative values?

Yes, the slope and y-intercept can have negative values. A negative slope means that the line is decreasing from left to right, while a negative y-intercept means that the line crosses the y-axis below the origin (0,0). This can be seen in equations such as y=-2x+5, where the slope is -2 and the y-intercept is 5.

## 5. How does the slope and y-intercept affect the graph of a line?

The slope and y-intercept have a significant impact on the graph of a line. The slope determines the steepness of the line, with a larger slope resulting in a steeper line. The y-intercept determines the position of the line on the y-axis, with a higher y-intercept resulting in a line that is higher on the y-axis. Together, the slope and y-intercept help us understand the direction, steepness, and position of a line on a graph.

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