Which equation represents the line that is perpendicular to y=1/4 and passes through (-6,9)? A. X= -9 B.x= -6 C.y= -9 D.y= -4

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asked Feb 13, 2023 136k views

2 Answers

Thlgood · Answer 1 · 2023-02-15T09:03:10+0000

$\huge\boxed{\boxed{\boxed{\bf{Hi\:there!}}}}$

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, change its sign, and flop it over.

Here, we have 1/4.

First, we change its sign:

-1/4

Now, we flop it over:

-4

So the slope of the line perpendicular to the given line is -4.

Now, we are given the slope of the line and a point that the line passes through.

We can use the Point-Slope formula:

$\huge\sf{y-y1=m(x-x1)$

$\huge\sf{y-9=1/4(x-6)$

$\huge\sf{y-9=1/4x-1.5$

$\sf{y=1/4x-1.5+9\\$

$\sf{y=1/4x+10.5$

$\huge\boxed{Hope\:it\:helps!}$

$\huge\bold{\underline{Good\:luck!}}$

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