Write an equation of the line that passes through (1,-4) and is perpendicular to the line: y = 2x + 5. Could anyone explain how to solve this? Thank you.

Question

texaschic101 · Answer

Look at your equation y = 2x + 5. First we need to find the slope. In y = mx + b form, the slope is in the m position. So can you tell me the slope of this equation ?

anonymous · Answer

The slope of the existing line is 2 and I know that since I'm trying to find the equation of a line that's perpendicular to y = 2x + 5 the slope of the perpendicular line would be -1/2. I don't know much beyond that.

texaschic101 · Answer

cool...you got that much correct.

Now their is 2 different ways to continue...
We can either use y = mx + b form or we can use y - y1 = m(x - x1).
I , myself, prefer the y = mx + b form (slope intercept form) unless specifically asked for the other y - y1 = m(x - x1), point slope form.

So we will use y = mx + b
we already know we need to use slope -1/2.
and our points (1,-4)....x = 1 and y = -4
now we will sub....we are looking for the y intercept (b)
y = mx + b
-4 = -1/2(1) + b
-4 = -1/2 + b
-4 + 1/2 = b
-8/2 + 1/2 = b
-7/2 = b

so your perpendicular equation is : y = -1/2x - 7/2

if you have any questions, please ask

texaschic101 · Answer

that is the answer in slope intercept form, but if you need it in standard form, let me know and I will continue

anonymous · Answer

That's all I need, thanks so much for your help.

texaschic101 · Answer

no problem...glad to help :)