Question

How can you graph the distance between y = -3/4x - 1
3x + 4y = 20

Answer 1

Please note the first equation should be y=-3x/4-1 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 y-axis]. 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