What is the distance between the lines 3x+4y=9 and 6x+8y=15?
You should check if the lines are paralle, hence you need to verify if the ratios of corresponding terms are the same such that:
`3/6 = 4/8 =gt 1/2 = 1/2`
Since these ratios are equal, then the lines are parallel.
You may also select a point that lies on the line `3x+4y=9` such that:
`(0,9/4)` lies on the line if `3*0 + 4*(9/4) = 9` .
You may evaluate the distance from the point `(0,9/4)` to the line `6x+8y=15 ` such that:
`d = |6*0 + 8*(9/4) - 15|/(sqrt(6^2 + 8^2))`
`d = 3/sqrt100 =gt d = 3/10`
Hence, evaluating the distance between the lines yields `d = 3/10.`
check Approved by eNotes Editorial