write the standard fourm of the equation that is parallell to 2x+5y=15and goes through (4,-2)

Answer 1

Greetings! Lets solve this shall we?

So, we must find the equation of a line parallel to the given line passing through the given point (4,-2) such that

2x+5y=15

5y = -2x+15

y = (-2/5)x + (15/5)

y = (-2/5)x + 3

Then we find the new line parallel using the point - slope formula such that

y - y1 = m(x-x1)

y - (-2) = (-2/5)(x - 4)

y + 2 = (-2/5)x + (8/5)

y = (-2/5)x + (8/5) - 2

y = (-2/5)x + (8/5) - (10/5)

y = (-2/5)x - (2/5)

I hope this helped!

Answer 2

2x + 5y = 15 => 5y = -2x + 15 => y = (-2/5)x + 3

The slope of this line and the line parallel to it is (-2/5)

The equation is (-2/5) = (y + 2)/(x - 4)

-2x + 8 = 5y + 10

In standard form: -2x - 5y = 10 or 2x + 5y = -10