SOLUTION: Write the equation of the line perpendicular to 9x + 2y = 18 and passes through the point (1, 4).

Question 199963: Write the equation of the line perpendicular to 9x + 2y = 18 and passes through the point (1, 4).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

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

Distribute

Multiply

Add 4 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

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

is .

If you want the equation in standard form, then the equation 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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