SOLUTION: Find the distance between the parallel lines corresponding to y=2x+3 and y=2x+7.

Question 189370: Find the distance between the parallel lines corresponding to y=2x+3 and y=2x+7.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Both of these equations have a slope of 2, so any line perpendicular to them will have a slope of

because:

And the distance between two parallel lines is the measure of a line segment that is part of a line that is perpendicular to the two lines and whose end points are the points of intersection between the perpendicular and each of the parallels.

Now that we have the slope of the perpendicular, we just need to choose an intercept to be able to write the equation of the perpendicular. Since any of the infinite number of lines available will solve our problem, let's pick the easiest in terms of the arithmetic that we will need to do. That would be the line with a slope of

and a y intercept of zero. The desired equation for the perpendicular is then:

Now we need the two points of intersection. You have two systems of two linear equations, namely:

and

Use the substitution method to solve each of these systems for the points of intersection. Once you have the two points,

and

, you can use the distance formula to find the distance between the two points and therefore the distance between the two parallel lines:

John

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