10th grade
posted by Chubby
How can you graph the distance between y = 3/4x  1
3x + 4y = 20

Ajit
Please note the first equation should be y=3x/41 if it is to represent a stright line. Now the two given lines are: y=  3x/4 ¨C 1 and 3x+4y=20 or y=3x/4 + 20. For us to calculate the distance between the two lines, they have to be parallel which they are since their slopes are equal viz. 3/4. [Recall y=mx+c where m = slope and c = intercept on the yaxis]. Now consider the line y=4x/3 which passes through the origin and has a slope of 4/3. This line is perpendicular to our earlier lines (Why?) and meets the former in A:(12/25,16/25) and the latter in B:(12/5,16/5). The distance AB which is the required distance between the two given lines =
sqrt[(12/5+12/25)^2+(16/5+16/25)^2]= 24/5
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