SOLUTION: My grandson needs help and I am lost: find the slope of any line that is perpendicular to the line 5x-2y=12. what are the steps??

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Question 275632: My grandson needs help and I am lost:
find the slope of any line that is perpendicular to the line 5x-2y=12. what are the steps??
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Start by determining the slope of the line represented by your given equation. To do that, put the given equation into slope-intercept form. To do that, solve the equation for in terms of everything else. For your problem, add to both sides of the equation and then multiply both sides of the equation by . The slope of the line represented by the given equation will then be the resulting coefficient on .

The slopes of perpendicular lines are negative reciprocals. That is to say:



So, once you have determined the slope of the line represented by the given equation, determine the negative reciprocal of that slope. If the slope is a fraction, turn the fraction over and change the sign.

John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is in the "standard form"
You need to get it in the "slope-intercept" form
which is:
y+=+mx+%2B+b
In this form, m is the slope
5x+-2y+=+12
Subtract 5x from both sides
-2y+=+-5x+%2B+12
Divide both sides by -2
y+=+%285%2F2%29%2Ax+-+6
Now it is in the slope-intercept form
where m+=+5%2F2
The rule is, that any line perpendicular to this line will have
slope = -%281%2Fm%29
-%281%2Fm%29+=+-%281%2F%285%2F2%29%29
-%281%2F%285%2F2%29%29+=+-%282%2F5%29
The slope of any line perpendicular to 5x+-+2y+=+12
is -%282%2F5%29