Answer: 2, 1.5 , -0.75
(b) [tex]4x-3y-10=0[/tex]
Step-by-step explanation:
Given
line is [tex]3x+4y-6=0[/tex]
Converting it into intercept form
[tex]\Rightarrow 3x+4y=6\\\\\Rightarrow \dfrac{3x}{6}+\dfrac{4y}{6}=\dfrac{6}{6}\\\\\Rightarrow \dfrac{x}{2}+\dfrac{y}{1.5}=1[/tex]
So, the x-intercept is [tex]2[/tex] and y-intercept is [tex]1.5[/tex]
The slope is given by
[tex]-\dfrac{\frac{1}{2}}{\frac{1}{1.5}}=-0.75[/tex]
(b) the line perpendicular to the above line and passing through [tex](1,-2)[/tex]
The slope of the required line
[tex]m=-\dfrac{1}{-0.75}\\\\m=\dfrac{4}{3}[/tex]
Equation of the line is given by
[tex]\Rightarrow \dfrac{y-(-2)}{x-1}=\dfrac{4}{3}\\\\\Rightarrow 3y+6=4x-4\\\Rightarrow 4x-3y-10=0[/tex]
