Question

Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6.

Answer 1

y = -5/3 * x - 40/3

Explanation:

A perpendicular line has an opposite and a reciprocal of the slope.

Your equation should be:

-5y = -3x +6

Divide all parts by -5.

y = 3/5x - 6/5

Since the perpendicular line has an opposite and a reciprocal of the slope, the slope will be -5/3.

Now you must make an equation in point-slope form. This is an example of that form. You will need at least one point to make this equation work. In this case we have (-8,0).

In put the y and x coordinates like this:

y - 0 = -5/3(x - (-8)

Start solving the equation.

y - 0 = -5/3(x + 8)

y - 0 = -5/3 * x - 40/3

y = -5/3 * x - 40/3

This is your equation.

y = -5/3 * x - 40/3

(You can make it -5/3x in your answer but it looks weird online. You may think that it is -5 divided by 3 times x, but it actually is 5/3 times x. That's why I wrote it as y = -5/3 * x - 40/3)

Answer 2

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Answer:

5x +3y = -40

Explanation:

When the equation of a line is given in standard form, the equation of the perpendicular line can be found by swapping the coefficients of x and y, and negating one of them.

Here, that means the equation ...

3x -5y = constant

becomes

5x +3y = new constant

The value of the new constant is found by putting the given point coordinates in the expression on the left:

5x +3y = 5(-8) +3(0) = -40

The equation of the perpendicular line is ...

5x +3y = -40