Second-degree Equation Step 1. Copy the given table on your graphing paper, after your student details. X (% concentration) 0.50 1.00 1.50 2.00 2.50 3.00 Y (oil separation) 5.10 3.60 2.60 2.00 1.40 1.00 Log Y Step 2. Initially plot the x and y values on a regular graphing paper (or millimeter graphing paper - if available, preferred for precision). Label then connect the points to observe curved line. Step 3. Since the line is curved, the y-intercept cannot be easily determined because you can’t exactly determine the direction of the line once extrapolated. To obtain a straight line, first, compute the logarithm values of all the y values up to the 2nd decimal place (for the purpose of easy plotting later) and fill in the table. Step 4. On another graphing paper, plot then label the x and log y. Using a dotted line, extrapolate the straight line to the y-axis. Label this point as “a” for the y-intercept. Step 5. For uniformity of answers, mark the first and second values in the table as (X1, log Y1) and (X2, log Y2) respectively for the computation. Compute for the slope of the line (b) using the formula: b = log y2−log y1/x2−x1 Step 6. Compute for the y-intercept using the modified two-point form of the linear equation line: log y – log y1= log y2−log y1/x2−x1 (x – x1), where y is the unknown. Input the complete value of the compute slope to this formula. The computed value should verify if the value of “a” is near or the same to the computed value. Step 7. Complete the statement for the interpretation: The data observes a second-degree equation, where the plotted X and Y values formed a curved line. To correct for this error, the y values were logged t, replotted with the value of x, obtain a straight line. The values of x and y are ______ (directly or inversely) proportional, where the computed slope is ______ (value rounded-off to the 3rd decimal place) and the y-intercept as ______ (value rounded-off to the 3rd decimal place).
Second-degree Equation
Step 1. Copy the given table on your graphing paper, after your student details.
X (% concentration) 0.50 1.00 1.50 2.00 2.50 3.00
Y (oil separation) 5.10 3.60 2.60 2.00 1.40 1.00
Log Y
Step 2. Initially plot the x and y values on a regular graphing paper (or millimeter graphing paper - if available, preferred for precision). Label then connect the points to observe curved line.
Step 3. Since the line is curved, the y-intercept cannot be easily determined because you can’t exactly determine the direction of the line once extrapolated. To obtain a straight line, first, compute the logarithm values of all the y values up to the 2nd decimal place (for the purpose of easy plotting later) and fill in the table.
Step 4. On another graphing paper, plot then label the x and log y. Using a dotted line, extrapolate the straight line to the y-axis. Label this point as “a” for the y-intercept.
Step 5. For uniformity of answers, mark the first and second values in the table as (X1, log Y1) and (X2, log Y2) respectively for the computation. Compute for the slope of the line (b) using the formula: b = log y2−log y1/x2−x1
Step 6. Compute for the y-intercept using the modified two-point form of the linear equation line: log y – log y1= log y2−log y1/x2−x1 (x – x1), where y is the unknown. Input the complete value of the compute slope to this formula. The computed value should verify if the value of “a” is near or the same to the computed value.
Step 7. Complete the statement for the interpretation: The data observes a second-degree equation, where the plotted X and Y values formed a curved line. To correct for this error, the y values were logged t, replotted with the value of x, obtain a straight line. The values of x and y are ______ (directly or inversely) proportional, where the computed slope is ______ (value rounded-off to the 3rd decimal place) and the y-intercept as ______ (value rounded-off to the 3rd decimal place).
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