Question

If the x-intercept of some line $L$ is double as that of the line, $3x+4y=24$ and the y-intercept of $L$ is half as that of the same line, then the slope of $L$ is

Answer 1

$3x+4y=2y$

$\frac{3x}{2y}+\frac{4y}{2y}=1$

$\frac{x}{8}+\frac{y}{6}=1$

If x intercept is doubled $=(2a,0)$

$(2\times 8,0)=(16,0)$

$(x_1,y_1)=(16,0)$

If y intercept is halved $=(0,\frac{b}{2})$

$=(0,\frac{6}{2})=(0,3)$

$(x_2,y_2)=(0,3)$

Intercept form,

$(y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$(y-0)=\left(\frac{3-0}{0-16}\right)(x-160)$

$y=\frac{-3}{16}(x-16)$

$\frac{-3}{16}x+3$

So, slope is $\frac{-3}{16}$