GOAL: Create equations of lines using Point Slope Form (P.S.F.) and convert it into Slope Intercept Form (S.I.F) Recall: Slope intercept form: There is another form of a line called Point Slope Form (P.S.F.) Where the is the slope And is any point on the line and are variables P.S.F. has the advantage of being able to write the equation quickly and easily because you’re not going through the work to find “ ”. EX: Find the equation of the line in P.S.F. passing through the given points. 1) A(2,1) and B(5,-6) We still the slope for either form… Now we can write the formula using either (2,1) (in other words ) or using (5,-6) Both are valid! 2) C(4,-3) and D(-9,-1) We still the slope for either form… Now we can write the formula using either (4,-3) (in other words ) or using (-9,-1) Both are valid! EX: Write the equation of the line in P.S.F. with slope and passing through (6,-8) We already have the slope, and the point. That’s all we need for P.S.F. To convert from Point Slope Form (P.S.F.) to Slope Intercept Form (S.I.F.) a. Distribute the slope b. Isolate the EX: Convert the following equations of a line from P.S.F. to S.I.F. and then state the y-intercept. 1) The y-intercept is (0,22) 2) The y-intercept is (0,-8.5) 3) The y-intercept is (0,79.54) EX: Create the equation of the line which passes through the points A(2.1, 1.9) and B(-2.8, 3.5) in P.S.F. Then convert it into S.I.F. P.S.F. Using (2.1, 1.9) S.I.F.: EX: Consider Data Set 5 5. Calcu-Chem Calcu-Chem produces a drug, which eliminates migraine headaches. The following table provides guidelines for dosage, and maximum dosage (measured in milligrams) for a patient’s weight (measured in pounds). Patient ID A B C D E F G H I J K L Weight (lbs) 88 99 110 121 132 143 154 165 176 187 198 209 Suggested Dose (mg) 40 45 50 55 60 65 70 75 80 85 90 95 Maximum Dose Allowed (mg) 66 75 83 91 100 108 116 125 133 141 150 158 Create an equation of a fit line in P.S.F. using Patient A and Patient F (suggested dose). Then convert it into S.I.F. and verify the y-intercept by looking at the graph. Our points are (88,40) and (143,65) P.S.F. Using (88,40) Converting to S.I.F. The y-intercept seems to be zero. Look at the graph again ?!?!? You might say “Hey! The y-intercept looks to be closer to 20!” But are you really looking at the y-axis? Notice the graph starts at . If the graph “extended” to the left far enough you could see it probably would hit the y-axis at the origin. Here is a version of the graph with the axis extended a bit.
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