Algebra2 Part12 Chapter1

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Example 1.20 Write the equation of the line passing through the points (-3,6) and (9, -10). Solution First find the slope of the line. m = triangle of y/ triangle x = -10-6/9-(-3) = -16/12= -4/3 Now choose either point and use the point-slope formula. Using the point (-3,6) gives y-6 = -4/3 (x + 3). Using the point 9, -10 gives y +10 = -4/3 (x -9). We seem to have two different answers to the same question. Both are correct and, if multiplied out and simplified, both are equivalent to y = -4/3 times x + 2. Common Error 9-(-3)/-10-6 = 12/-16= -3/4 is wrong. Be sure to put the y-values on top (in the numerator) and the x-values on the bottom (in the denominator) of the slope fraction. Common error 10-6/-3-9 = -16/-12 = 4/3 is wrong. Watch the order of subtraction. One set of ordered pairs must be subtracted from the other set of ordered pairs. Example 1.21 Graph the line y +4 = 10/7(x-1) Solution You can rewrite the line in y = mx + b form, but the y-intercept turns out to be an inconvenient -38/7. In stead, it is easier to note that the line has slope 10/7 and passes through the point (1,-4). (Note that the signs of the coordinates of the point are the opposite of the signs in the equation. Get used to that, You will see it again in other chapters.) Plot (1,-4). Then count "up 10, right 7" from there to find a second point. x and y meet in the middle on the left side . The equation line runs in the middle if the cubes and through the middle of the x line and through the lower part of the y line. The equation is y + 4 = 10/7(x-1). Common Error Starting at ( -4,1) is wrong. Don't be fooled by the order in which the numbers appear in the equation. The value for the x-coordinate is next to x in the equation. The value for the y-coordinate is next to y in the equation. Example 1.22 Two minutes after an oven is turned on, its temperature is 115- degree Fahrenheit and is increasing at a rate of 24degreeF each minute. Write a linear equation to model the temperature in the oven as a function of time in minutes since the oven w.as turned on. Solution Let t represent time in minutes since the oven was turned on and T represent the temperature in the oven in degrees F. At time t = 2 minutes, the temperature was 115-degree F. So, we know one point (2,115). The rate of change of temperature, 24-degree F per minute, is the slope. We can use the point slope formula. T-115 = 24(t-2) This equation can be left as is or simplified T=24t +67(Continue)