Question

A) Find the slope, x-intercept, y-intercept of the line (L):

Answer 1

Answer: 2, 1.5 , -0.75

(b) $4x-3y-10=0$

Step-by-step explanation:

Given

line is $3x+4y-6=0$

Converting it into intercept form

$\Rightarrow 3x+4y=6\\\\\Rightarrow \dfrac{3x}{6}+\dfrac{4y}{6}=\dfrac{6}{6}\\\\\Rightarrow \dfrac{x}{2}+\dfrac{y}{1.5}=1$

So, the x-intercept is $2$ and y-intercept is $1.5$

The slope is given by

$-\dfrac{\frac{1}{2}}{\frac{1}{1.5}}=-0.75$

(b) the line perpendicular to the above line and passing through $(1,-2)$

The slope of the required line

$m=-\dfrac{1}{-0.75}\\\\m=\dfrac{4}{3}$

Equation of the line is given by

$\Rightarrow \dfrac{y-(-2)}{x-1}=\dfrac{4}{3}\\\\\Rightarrow 3y+6=4x-4\\\Rightarrow 4x-3y-10=0$