Question

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

Answer 1

Answer on Question #83168 – 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, so we find the slope(m) of $2y + 3x = 3$

$$\begin{array}{l} 2y + 3x = 3 \\ 2y = -3x + 3 \\ y = -3/2x + 3/2 \\ y = -1.5x + 1.5 \\ m = -1.5 \\ \end{array}$$

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

$$\begin{array}{l} x1 = -2 \quad x2 = 4 \quad x0 = (-2 + 4)/2 = 1 \\ y1 = 3 \quad y2 = 5 \quad y0 = (3 + 5)/2 = 4 \\ \end{array}$$

Equation of the 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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