What is the distance between the lines 3x+4y=9 and 6x+8y=15?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.`

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