Question 536509
Are they parallel, perpendicular, or neither?
1) {{{5x-6y = 19}}} and...
2) {{{6x+5y = -30}}}
First, put both equations in the "slope-intercept" form: {{{y = mx+b}}}
{{{5x-6y = 19}}} Add 6y to both sides.
{{{5x = 6y+19}}} Now subtract 19 from both sides.
{{{5x-19 = 6y}}} Finally, divide both sides by 6.
{{{(5/6)x-19/6 = y}}} or
{{{y = highlight((5/6))x-19/6}}}
Similarly for equation 2)
{{{6x+5y = -30}}} Subtract 6x from both sides.
{{{5y = -6x-30}}} Now divide both sides by 5.
{{{y = highlight_green((-6/5))x-6}}}
Compare with the "slope-intercept" form:
{{{y = mx+b}}} where m is the slope.
{{{m[1] = 5/6}}} and...
{{{m[2] = (-6/5)}}}
You'll notice that the slopes are negative reciprocals of each other!
If two lines are perpendicular, their slopes are the negative reciprocal of each other.
What's your conclusion?