SOLUTION: Hello, I would like help on this problem: I need to write the point (-5,3) and perpendicular to the graph of 2x + 6y =7 in the standard form of ax + by = c I am confused on th

Question 659049: Hello, I would like help on this problem:
I need to write the point (-5,3) and perpendicular to the graph of 2x + 6y =7 in the standard form of ax + by = c
I am confused on the steps and not sure if I'm solving it right.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
convert the original equation to point slope form by solving for y.
2x + 6y = 7
subtract 2x from both sides to get:
6y = -2x + 7
divide both sides by 6 to get:
y = (-2/6)x + (7/6)
the equation is in slope intercept form with a slope of (-2/6) and a y intercept of (7/6).

your new line is perpendiculat to this so the slope of the new line has to be naegative reciprocal of the original line.

this makes the slope of the new line equal to 6/2 = 3.

the slope intercept form of the new line is equal to y = 3x + b
b is the y intercept that we haven't solved for yet.

the point (-5,3) goes through this line.

substitute (-5) for x and 3 for y and solve for b.
you get y = 3x + b becomes 3 = 3(-5) + b which becomes 3 = -15 + b
add 15 to both sides of this equation to get b = 18.

the equation of the line perpendicular to the original line and passing through the point (-5,3) is y = 3x + 18.

you now have 2 equations which you can graph to see how you did.
they are:
y = -(2/6)x + (7/6) and y = 3x + 18
their graphs are shown below:

they look perpendicular and the graph is squared so we're probably ok.

what is left is to convert the equations back to standard form.

we'll do the original equation first.
y = (-2/6)x + (7/6) is the slope intercept form.
add (2/6)x to both sides of the equation to get:
(2/6)x + y = (7/6)
multiply both sides of the equation by 6 to get:
2x + 6y = 7
if you remember correctly, this is the original equation in standard form so we're good to go.

now we'll do the perpendicular equation.
that equation is in slope intercept form and is shown on the next line:
y = 3x + 18
subtract 3x from both sides of the equation to get:
-3x + y = 18
this is in standard form except it's customary to show the x variable as positive.
if we multiply both sides of this equation by -1 we can achieve that without changing the equality.
the equation becomes:
3x - y = -18
if you converted this modified equation back to slope intercept form it should be identical to what it was before.
we'll do that just to show you.
subtract 3x from both sides of the equation to get:
-y = -3x - 18
multiply both sides of the equation by -1 to get:
y = 3x + 18
the slope intercept form is identical to what it was before so we're still good to go.
for the standard form of the equation you should be able to use either:
-3x + y = 18 or:
3x - y = -18
check with your instructor on what he or she expects in this case.

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