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Class Notes on Unit AE: Solving Literal Equations D = rt is a formula for distance traveled by an object going at a rate of r for a time of t. If r is 60 miles per hour and time is 3 hours then distance is 60(3) or 180 miles. If the distance traveled was 300 miles and the time was 6 hours one could solve the equation 300 = r(6). The solution is 50 miles per hour. One could also take the formula D = rt and solve for r. Then you would have a formula for rate. D = rt To “solve for r”, you must isolate r on one side of the equation. D rt Divide each side of the equation by t. Because we = do not know the value of D and t, we cannot actually t t do the division. Instead we just show D divided by t. D D = r Now we have a formula for Rate. r = or Rate is equal to t t Distance divided by Time. y = mx + b is called the slope-intercept formula for the graph of a line. m is the line’s slope. (0,b) is the line’s y-intercept. (x,y) represents the coordinates of any point on the line. If a line has a slope of –3 and (0,9) is it’s y-intercept, the equation of the line in slope-intercept format is y = -3x + 9. Suppose that we wanted a formula for the slope of the line. One could solve for m as follows: y = mx + b To “solve for m”, you must isolate m on one side of the equation. y – b = mx Begin by subtracting b on both sides of the equation. y b =m Now divide each side of the equation by x. x y b This is a formula for the slope of a line where (x,y) is any point on m= the line where the x-coordinate is not zero, and b is the y- x coordinate of the y-intercept. Try theses1: a. a + b = c Solve for b. b. q = pt – s Solve for t. 1 q s a. b=c–a b. t = p AE-2 Suppose (1,3) is a point on a line and (0,5) is the line’s y-intercept. Find the slope of this line Write the equation of the line in slope-intercept form. y b Take the formula for m= slope. y = mx + b Take the slope-intercept x formula for a line. 3 5 Substitute the values Substitute the values of m= given for x, y and b. y = -2x + 5 m and b. Note that (x,y) 1 Evaluate. represents any point on m = -2 The slope is -2 the line. In order to sketch a graph using a graphing calculator or using certain by hand methods, one has to “solve for y.” Here is an example with a linear equation. 2x + 3y = 12 The goal is to put the equation in the form y = mx + b. 3y = -2x + 12 First subtract 2x on both sides of the equation. 3y 2x 12 = Divide both sides of the equation by 3. 3 3 3y 2x 12 = + Make into two fractions (reverse of addition) 3 3 3 2 y = - x + 4 Reduce constant and separate coefficient from the variable x. 3 c. Solve2 for y: -6x + 4y = -28 c. Solve3 for y: -3x - 4y = -12 2 c. y= 3x - 7 2 3 c. y=-3x + 3 4

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posted: | 3/2/2010 |

language: | English |

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