Mx+b

[Barb Frison]

Tofind the value of m, you need to identify the slope of the line. The slope can be calculated by dividing the change in y-coordinates by the change in x-coordinates between two points on the line. Once you have the slope value, you can substitute it into the equation y = mx+b to solve for m.

The y-intercept, represented by the value of b in the equation, indicates the point where the line intersects with the y-axis. It is the starting point of the line and can be used to determine the initial value or y-coordinate when x=0.

No, only linear equations can be expressed in y = mx+b form. Linear equations are those with a constant rate of change between the variables. Non-linear equations, such as quadratic or exponential equations, cannot be written in this form.

To check if an equation is in y = mx+b form, you can rearrange it to see if it follows the standard format. The variable y should be isolated on one side of the equation, with the slope (m) and y-intercept (b) on the other side. Additionally, the coefficient of x should be equal to the slope value (m).

Putting an equation into y = mx+b form makes it easier to graph and interpret the equation. The slope and y-intercept can be directly read from the equation, allowing for quick and accurate graphing. It also allows for easier comparison and analysis of multiple equations with the same form.

Graph lines using a slope and a y-intercept. Identify the slope and y-intercept from the equation of a line in slope-intercept form. This activity is useful for algebra students learning to graph lines for the first time, or for students who may need extra help or review with this topic. y=mx+b is the second of seven activities for teaching and learning linear equations in algebra: Ski Slope; y=mx+b; Points, Intercepts, and Slopes, Oh My!; Linear Equations Word Problems; Solving Systems of Equations; Systems of Equations Word Problems Part 1; Systems of Equations Word Problems Part 2.

Slope is derived from the Latin root slupan for slip. The relation seems to be to the level or ground slipping away as you go forward. The root is also the progenitor of sleeve (the arm slips into it) and, by dropping the s in front we get lubricate and lubricious (a word describing a person who is "slick", or even "slimy").

Many variations of where the idea of M for slope originated seem to be mostly myth. One of the most common is that the letter was used by Descarte because it was the first letter of some French word or another that related. In a recent post to the AP Stats discussion list, Hector Hirigoyen shared the following story:

I was told by Mary Dolciani herself, that the SMSG group "decided "to use y=mx+b because of the French (Descartes, I presume)-"montant"; I found it strange because the "logical word" would be "pente"(which is slope (and the standard term in Spanish is pendiente, which matches this). However, several years ago, while visiting a French high school, I noticed the teacher used y=sx+b. I inquired, and she said because of the "American" word "slope." I believe they are using ax+b for the most part these days.

In his "Earliest Uses of Symbols from Geometry" web page, ... Jeff Miller gathered the following information: Slope. The earliest known use of m for slope is an 1844 British text by Matthew O'Brien entitled _A Treatise on Plane Co-Ordinate Geometry_ [V. Frederick Rickey]. George Salmon (1819-1904), an Irish mathematician, used y = mx + b in his _A Treatise on Conic Sections_, which was published in several editions beginning in 1848. Salmon referred in several places to O'Brien's Conic Sections and it may be that he adopted O'Brien's notation.

According to Erland Gadde, in Swedish textbooks the equation is usually written as y = kx + m. He writes that the technical Swedish word for "slope" is "riktningskoefficient", which literally means "direction coefficient," and he supposes k comes from "koefficient." According to Dick Klingens, in the Netherlands the equation is usually written as y = ax + b or px + q or mx + n. He writes that the Dutch word for "slope" is "richtingscoefficient", which also means "direction coefficient." In Austria k is used for the slope, and d for the y-intercept. In Uruguay the equation is usually written as y = ax + b or y = mx + n, and the "slope" is called "pendiente", coeficiente angular", or "parametro de direccion".

It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for "to climb" is monter. However, there is no evidence to make any such connection. Descartes, who was French, did not use m. In _Mathematical Circles Revisited_ (1971) mathematics historian Howard W. Eves suggests "it just happened."

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