Question

Find the equation of the line passing through ($-$3,$-$5) and parallel to x $-$ 2y $-$ 7 = 0

Answer 1

The given equation of line is x $-$ 2y$-$7 = 0.

Slope of the line = $\frac{-\mathrm{coefficient}\mathrm{of}x}{\mathrm{coefficient}\mathrm{of}y}=\frac{-1}{-2}=\frac{1}{2}$
The required line is parallel to the line x $-$ 2y$-$7 = 0 and we know that parallel lines have equal slopes.
Hence, slope of the required line, m = $\frac{1}{2}$ and the point ($-$3, $-$5) lies on the required line.
So, the point slope form of the equation is
y $-$y₁ = m (x $-$ x₁)
⇒ y$-$ ($-$ 5) = $\frac{1}{2}${x $-$ ($-$3)}
⇒ y +5 = $\frac{1}{2}$(x + 3)
⇒ 2y + 10 = x + 3
∴ x $-$ 2y $-$ 7 = 0, which is the required equation.