Question

in each case, determine ( k ) so that the line is parallel to the line ( 2x - 4y + 25 = 0 )
(a) ( 4x + ky = 8 )
(b) ( kx - 2y - 4 = 0 )
(a) what value of ( k ) will make ( 4x + ky = 8 ) parallel to ( 2x - 4y + 25 = 0 )?
( k = ) \\( \square \\) (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Rewrite lines to slope-intercept form

First, rewrite $2x - 4y + 25 = 0$:
$-4y = -2x -25$
$y = \frac{1}{2}x + \frac{25}{4}$
Rewrite $4x + ky = 8$:
$ky = -4x + 8$
$y = -\frac{4}{k}x + \frac{8}{k}$ (for $k
eq 0$)

Step2: Set slopes equal (parallel lines)

Parallel lines have equal slopes, so:
$\frac{1}{2} = -\frac{4}{k}$

Step3: Solve for k

Cross-multiply to isolate k:
$k = -4 \times 2$
$k = -8$

Answer:

$-8$