Writing equations

Question

Wrong wan equation of the line that passes through the given point and is perpendicular to the graph of the given equation (3,-6); x+y=-4

Answer 1

Here is an alternative way to do it which I like and because they don't specify in what form the answer should be.

For a perpendicular line 'reverse' the slope and change x + y to x - y and just say x - y = C

Now put in the point (3,-6) to find C

3 - (-6) = C

C = 9

x - y = 9

In slope intercept form that would be y = x - 9

Answer 2

Given point: (3, -6)

Given line: x + y = -4

First we have to convert our given line into y = mx + b form. We have to solve for y.

x + y = -4

-x -x

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y = -x + 4

That means that the slope for the given line is -1.

Since we are looking for a line that is perpendicular, that means the slope

will be opposite and the reciprocal of the given slope.

This means the new slope will be 1.

Now we use out point slope formula and plug in the new slope and the point we were given:

y - y₁ = m(x - x₁)

y - (-6) = 1(x - 3)

y + 6 = x - 3

-6 -6

y = x - 9

So the equation that is perpendicular to x + y = -4 and passes through the point (3, -6) is

y = x - 9