Question

Find the equation of the line which is parallel to the 2y+3x=3 and passes through the midpoint (-2,3) and (4,5)

Answer 1

Answer on Question #83045 – Math – Analytic Geometry

Question

Find the equation of the line which is parallel to the $2y + 3x = 3$ and passes through the midpoint $(-2, 3)$ and $(4, 5)$

Solution

Parallel lines have equal slopes, therefore we find the slope $m$ of $2y + 3x = 3$:

$$2y + 3x = 3$$ $$2y = -3x + 3$$ $$y = -\frac{3}{2}x + \frac{3}{2}$$ $$y = -1.5x + 1.5$$ $$m = -1.5$$

Thus, the slope of the line parallel to the $2y + 3x = 3$ also will be $m = -1.5$.

The midpoint between two points is $((x1 + x2)/2, (y1 + y2)/2)$

$$x1 = -2, \quad x2 = 4, \quad x0 = (-2 + 4)/2 = 1,$$ $$y1 = 3, \quad y2 = 5, \quad y0 = (3 + 5)/2 = 4.$$

Equation of the unknown line is

$$(y - y0) = m(x - x0)$$ $$(y - 4) = -1.5(x - 1)$$ $$y = -1.5x + 5.5$$ $$2y + 3x = 11$$

Answer: $2y + 3x = 11$

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