Question

Identify which equation represents a line perpendicular to the given equation 2x+5y=25

Answer 1

y = 5/2x + 5

y = 5/2x - 9.5

Explanation:

We need to solve for the y in the expresion of 2x + 5y = 25

`2x + 5y = 25\\y = (25 - 2x)/5 \\y = 5 - 2/5x`

now we re-arrenge the factors in the form y = ax + b

y = -2/5x + 5

we reverse "a"

y = 5/2 + a

And now, we use a point in the other formula to solve for a:

original line:

y = 5 - 2/5x

X = 0 then Y = 5

now we solve for the general equation of the perpendicular equation:

`y - y_1 = m ( x - x_1)`

`y - 5 = 5/2 (x - 0)\\y = 5/2x + 5`

If we use a different point we get a different formula:

original line:

y = 5 - 2/5x

X = 5 then Y = 3

`y - 3 = (5)/(2)(x - 5)\\y - 3 = (5)/(2)x -12.5 \\y = (5)/(2)x - 9.5`

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