Question 911953
The lines with equations 5x+3y=4 and 2kx-5y=10 are perpendicular
what is the value of k?
:
Put both equations in the slope intercept form
5x + 3y = 4
3y = -5x + 4
y = {{{-5/3}}}x + {{{4/x}}}
:
2kx - 5y = 10
-5y = -2ks + 2
Divide both sides by -5
y = {{{2k/5}}}x - 2
:
The slope relationship of perpendicular lines: m1 * m2 = -1, therefore:
{{{-5/3}}} * {{{2k/5}}} = -1
{{{(-10k)/15}}} = -1
multiply both sides by 15
-10k = -15
k = -15/-10
k = +1.5
Therefore the 2nd equation:
y = {{{(2*1.5)/5}}}x - 2
y = {{{3/5}}}x - 2
:
;
See if the relationship between the two slopes is -1
{{{-5/3}}} * {{{3/5}}} = -1