Find the equation of the parallel to the line 3x-2y=5 and passing through the midpoint of the line segment joining the points (-4,2) and (2,4).​

Given:

The equation of parallel line is:

The required line passing through the midpoint of the line segment joining the points (-4,2) and (2,4).​

To find:

The equation of required line.

Solution:

Midpoint of  line segment joining the points (-4,2) and (2,4) is:

It means the required line passes through the point (-1,3).

The slope of line is:

The given equation is:

Here, A=3 and B=-2. So, the slope of the line is:

Slope of parallel lines are same. So, the slope of the required line is 1.5.

The required line passes through the point (-1,3) with slope 1.5. So, the equation of the line is:

Adding 3 on both sides, we get

Therefore, the equation of the required line is .

step-by-step explanation:

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