Question

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

Answer 1

Answer:

y = 5/2x + 5

y = 5/2x - 9.5

Step-by-step 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

$y - 3 = \frac{5}{2}(x - 5)\\y - 3 = \frac{5}{2}x -12.5 \\y = \frac{5}{2}x - 9.5$

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