Question 360482
Find "k" if the line 3x+ky=5 is parallel to the line 2x-7y=4.
Find the slope of 2x - 7y = 4, put in the slope/intercept form
-7y = -2x + 4
7y = 2x - 4; multiplied by -1
y = {{{2/7}}}x - {{{4/7}}}
:
slope = {{{2/7}}} we know parallel lines have the same slope
:
put 3x + ky = 5 in the slope/intercept form
ky = - 3x + 5
y = {{{-3/k}}}x + {{{5/k}}}
:
slopes are equal therefore:
{{{-3/k}}} = {{{2/7}}}
cross multiply
2k = -3 * 7
2k = -21
k = {{{-21/2}}}