Linear Functions Notes from Week #1

Rate of Change Rate of change is the ratio of the change in y values divided by the change in x values. Written as If the rate of change is a constant then the relationship is Linear. To determine if a table represents linear data find the ratio in the ∆y over the ∆x +2 +2 +4 X 1 3 5 9 Y 4 8 12 20 The rates of change all equal the same value so the relationship is linear +4 +4 +8

Slope The slope of a linear function is represented by the rate of change in the data, or when graphed, the vertical change from one point to the next divided by the horizontal change from the same points, or the steepness of the line. Slope =

Slope From a Graph To find the slope of a line from a graph you find the vertical change from one point to another point on the line know as the RISE. Rise = 3 Run =2 Then find the RUN which is the horizontal change between the same points • •

Slopes of Lines Negative slope Positive slope Undefined slope, “NO” slope, Infinite slope, ∞ Zero slope

The Slope Formula When given 2 points you can find the slope mathematically by using the slope formula. The slope is denoted by the variable “m” One of the many possible reasons for the letter “m” can be credited to Euler, a famous mathematician who has made many contributions to the mathematical world, including his book on the Elements. According to some documents, Euler used the letter “m” because it represented “modulus of slope,” which translated to the number used to measure the slope. Another explanation involves the French word “monter”, which means “to climb.” Both of these explanations involve the first letter of a particular word related to slope. Slope Formula When given the points ( x1, y1), ( x2, y2)

Computing the Slope Find the slope of the line containing the points ( 2, 5) , (4, 11) Using the slope formula It does not matter which point you start with you just need to keep the same order for both x and y or Students who struggle with adding and subtracting positive and negative numbers can put the points into a mini table and find the change in x and y values x y 2 5 4 11 +2 +6