Algebra2 Part10 Chapter1

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"You probably first learned 'slope' as "rise over run," which is represented graphically and in symbols in Figure 1.2" Using two lines (one with y on it) and (the other with x on it then forming a line with a specific 'Slope = m = Ay/AX = y to the 2 - y to the 1/ x to the 2 - x to the 1, you end up with a line drawn on a slope with a point at (x to the 1, y to the 1) in the lower corner and a higher dot at the top of the line (x to the 2, y to the 2 ) with a 'Run" dotted line triangle x = x to the 2 - x to the 1 reaching to the 'Rise" of a dotted line triangle y = y to the 2 - y to the first. Where they meat is a square angle. "There are two ways to think about a 'slope' You are probably already familiar with the idea that , graphically, 'slope' measures the steepness and direction of a line. Different categories of slopes are depicted in the following table." " Table 1.2 'Slope' of a Line" 1. "If the 'slope is 'positive'. the line is increasing (rising) from left to right' Larger 'slopes mean steeper lines (increasing faster)." shown by a few arrowed lines outward from the angle of the two side lines y and x opposite each other. The top line inside is marked m = 2, one in the middle-marked m = 1, and the lowest one marked m = 0.5 2. "If the 'slope' is negative, the line is decreasing (going down) from left to right. Slopes with larger absolute values have steeper lines (decreasing faster)" These three lines are running towards each line of x and y that are opposite of each other; one line is marked m = -0.5, the middle m = -1, the last or closest to the y, x angle marked as m = -2 "3. If the slope is 0, the line is 'horizontal'."(m = 0) 4. "The 'slope' of a 'vertical line' is 'undefined.' m undefined "The second interpretation of slope isn't always emphasized in Algebra 1 but is very important. "Slope i the 'rate og change of y with respect to x'. If a line has a slope of m, then each time x increases by one unit, y will change by m units." For example, If m = 2, then each time x increases by 1, y will increase by 2. If m = - 2/3, then each time x increases by 1 y will decrease (because of the negative sign) by 2/3." Example 1.16 "Suppose you are filing a swimming pool with water from a garden hose. You note that at 1 o'clock, the pool has 18 inches of water in it. At 5 o'clock. there are 32 inches of water in the pool. What is the rate of change of the depth of the water?(Find out in the next lesson)