Question

Determine the equation of a line parallel to y=-2x+7 with the same x intercept as 3y-4x=16.

Answer 1

Answer:

the equation intersect actually at 1 point

Answer 2

Answer:  2x + y = 8

Step-by-step explanation:

Let equation of line parallel to  $l_{2}$  => $y = -2x + 7$ be   $l_{1}$  => $y = mx + b$

Let slope of  $l_{1}$  and  $l_{2}$  be  $m_{1}$  and  $m_{2}$ respectively.

slope of $l_{2}$ = $m_{2}$ = $\frac{-2}{1}$ => -2

{ $l_{1}$ and $l_{2}$ are parallel } => $m_{1} = m_{2}$

                                     => $m_{1} = -2$      { $m_{2} = -2$ }

.: Equation of line ( SLOPE INTERCEPT FORM ) => y = mx + b

                                     Put $m_{1} = -2$                        => y = -2x + b ------------ ( 1. )

x - intercept of $3y - 4x = 16$

{ y = 0 } => $0 - 4x = 16$

            => $-4x = 16$

            => $x = -4$ = A

Put x - intercept x = -4 and y = 0 in ( 1. ) => $0 = -2( -4 ) + b$

                                                                 => $b = 8$

.: Equation of line  $l_{1}$  =>  2x + y = 8