Question

The equation of the line passing through $(2,0)$ and $(0,3)$ is $\frac{x}{2}+\frac{y}{3}=1$

• A. False
• B. True

Answer 1

The correct option is B

True

We know that the slope(m) of the line formed by joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

The given points are $(2,0)$ and $(0,3)$.

Then, slope, $m$=$\frac{3-0}{0-2}$$\frac{-3}{2}$

$\therefore$ Equation of the line is given by,

$y-y_1=m(x-x_1)$

$⟹y-0=\frac{-3}{2}(x-2)$

$⟹2y=-3x+6$

$⟹3x+2y=6$

$⟹\frac{3x}{6}+\frac{2y}{6}=1$

$⟹\frac{x}{2}+\frac{y}{3}=1$