Question

Write an equation in slope intercept form for the line that passes through (1,-4) and is perpendicular to the graph of 5x + 10y = 15

PLEASE HELP MEE! YOU GET A LOT OF POINTS!!!

Answer 1

Y=-2x-2

Explanation:

First of all we must start from this principle:

"Two lines with slopes other than zero are perpendicular if and only if the product of their slopes is -1."

This lead us to calculate the slope of the given line

`5X+10y=15`

if we divide this equation between 10 in order to isolate Y we get that:

`(1)/(2) X-Y=(3)/(10) \\ \\ then\\\\ Y=(1)/(2)X-(3)/(10)`

So, Having the equation in this form, its slope will always be the term that accompanies the X. In this case the slope of the given line is 1/2

Now, to comply with the principle of perpendicularity, we must find a number that when multiplied by 1/2 gives the result -1. This value will be the slope of the line we are looking for.

Then let's call that value "m" So,

`(1)/(2)m=-1`

m=-2 (This is the slope for the perpendicular line)

Now, We can proceed to calculate its equation:

`y-y_(0)=m(x-x_(0) )\\` knowing that (x0,y0)=(1,-4)

`y-(-4)=-2(x-1)`

`y+4=-2x+2`

`y=-2x+2-4`

`y=-2x-2`