What is the equation in standard form of a perpendicular line that passes through (5,1)? The line perpendicular points (5,1) is y=-4x+4

Question

lord_box · Answer

What's true about the slopes of perpendicular lines?

yoyo2443 · Answer

That their slopes are negative reciprocals...?

lord_box · Answer

So what would be the negative reciprocal of the slope of -4x + 4?

yoyo2443 · Answer

$$\frac{ 1 }{ 4 }$$

lord_box · Answer

Right, so you know the slope of the function, and a point on the function. You can construct an equation using this information.

yoyo2443 · Answer

I'm not sure how I would apply it for the standard form though because some information is missing (standard form is Ax + By= C x and y being the points and the rest.. I'm not so sure..)

lord_box · Answer

First, put it in point slope form, and we'll work it from there.

yoyo2443 · Answer

alright so.. $$y-1=\frac{ 1 }{ 4 }(x-5)$$

lord_box · Answer

Good, now take it to y = mx + b form.

lord_box · Answer

By first distributing the 1/4 and moving the -1 over you can accomplish this.

yoyo2443 · Answer

$$y-1=\frac{ 1 }{ 4 }x -1 \frac{ 1 }{ 4 }$$ something like that?

lord_box · Answer

Yes, move the -1 to the right side

yoyo2443 · Answer

$$y= \frac{ 1 }{ ?4}x - \frac{ 1 }{ ?4}$$ ?

yoyo2443 · Answer

... forgot to remove the question marks there... My bad

lord_box · Answer

Yeah, now just move the 1/4x to the left side and it should look familiar.

yoyo2443 · Answer

$$x \frac{ 1 }{ 4 }-y=\frac{ 1 }{ 4 }$$

lord_box · Answer

Looks good.

yoyo2443 · Answer

Awesome, thank you!

lord_box · Answer

You're welcome.