SOLUTION: Solve the following: Passing through (5,-9) and perpendicular to x + 7y = 12

Question 149331: Solve the following:
Passing through (5,-9) and perpendicular to x + 7y = 12
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Passing through (5,-9) and perpendicular to x + 7y = 12
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Find the slope of x + 7y = 12
Put in standard form y = mx+b
y = -x/7 + 12/7
Slope m = -1/7
The slope of a perpendicular line is +7.
y-y1 = m(x-x1)
y-(-9) = 7*(x-5)
y+9 = 7x-35
7x-y = 44
To check: 7*5 -(-9) = 44, so it does go thru the point (5,-9)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract x from both sides.

Divide both sides by 7.

Break up the fraction and simplify.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point .

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Subtract 9 from both sides.

Combine like terms.

So the equation of the line perpendicular to that goes through the point is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point .

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