Algebra2 Part11bChapter1

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Before we move forward, we have one more Example. Example 1.18 The speed of sound at sea level is a function of temperature. It can be modeled by the equation S = 0.60T + 331.45, where S is the speed in meters per second and T is the temperature in degrees Celsius. a. What is the rate of change of the speed of sound with respect to temperature? b. What does 331.45 represent in this problem? Solution a. Remember that rate of change of a line is the 'slope'. In this problem, the rate of change is 0.60 meters per second per degree Celsius. This means that for each increase of 1 degree C in temperature, the speed of sound increases by 0.60 meters per second. b. The number 331.45 is the s-intercept. It is the value of s when T = 0. So, when the temperature is 0 degree C, the speed of sound at sea level is 331.45 meters per second. 'Point-Slope Equation' of a Line "Given both the slope and the y-intercept of a line, it is easy to write the equation in 'slope-intercept form'. For example, if the slope is 0.75 and the y-intercept is 20, the equation is y = 0.75x + 20. if we know the slope and a point other than the y-intercept, the 'slope-intercept form' can still be used but it takes a little more work. For this kind problem, use the more convenient form of the equation of a line called the 'point-slope form'. The equation comes directly from the 'slope formula'. If 9x to the 1, y to the1 is a known point (x, y), then the formula is derived as shown in Figure 1.3'" The figure again shows that crossover of x, y lines with a line pointing into the angle and straight out with a known point (x to the 1, y to the 1) with a known slope, m and the other point ((x, y). With the formulas m = y- y to the 1/x - x to the first or y - ,y to the 1 = m(x- x to the first, the 'point-slope' equation of a line y -y to the 1 = m(x-x to the 1) where m is the slope, x to the 1, y to the 1) are the coordinates of a known point on the line "Some people prefer to use this equation with y by itself: y = m(x -x to the first) + y to the 1. Use whichever form you find easier to remember. Example 1.19 Write he equation of the line with slope = -1/2 that passes through the point (-4, 7) Solution Use the 'point-slope form. y- y to the 1 = m(x - x to the 1, with m = -1/2, x to the 1 = -4 and y to the 1 = 7 y - y to the 1 = m(x - xto the 1) y -7 = -1/2(x -(-4)) y -7 = -1/2(x + 4) some accept this answer but you can disribute the slope and add 7 to both sides to optain y= mx + b form.