What is the slope of the line passing through the point (4, -3) and perpendicular to the line y = 2x + 1? Write your answer as a fraction.

Question

roadjester · Answer

The slope of a perpendicular line will always be the negative reciprocal of the slope of the line given. Since the line given has a slope of 2, you want a slope of $$-1\over 2$$

roadjester · Answer

Next, do you know the point-slope formula? I'm not sure what you mean "write your answer as a fraction."

roadjester · Answer

y-y1=m(x-x1) Does that look familiar? Just do some algebraic manipulation to get the answer you want.

anonymous · Answer

thank you

anonymous · Answer

but there is only one point , so how would yo use the formula y-y1=m(x-x1) ?

roadjester · Answer

You have one point yes, but notice how in the line you gave you have an x and a y? (y=2x+1)

roadjester · Answer

Same situation, the x and y remain as variables.
The x1 and y1 come from the point given.

anonymous · Answer

so it would be 1- (-3)= -1/2 ( 2-4)

roadjester · Answer

actually no

roadjester · Answer

You're looking for a formula right?
That means that you NEED n x and a y. Otherwise you just have a number, not the equation of a line.
An equation of a line will always be y=mx+b. Which is slope-intercept form.

anonymous · Answer

yea so you only need the (4, -3) to find the slope of the line

roadjester · Answer

No, the slope of the line is - (1/2)
Your line can take three forms: standard, point slope, or y-intercept.
For our purposes, you have enough information for point-slope. (notice how it's point not points)

anonymous · Answer

so it would be y-(-3)= (-1/2)(x-4)

roadjester · Answer

BINGO. Now, you just need to do algebraic manipulation to get the answer you want since I don't really know what you mean by writing the answer as a fraction.

anonymous · Answer

but how would you solve it? because it would be 
y+3= (-1/2) (x-4)  
Solve for Y & X separately

roadjester · Answer

Well, I don't know what you mean by "Write your answer as a fraction."
That's the only issue.

roadjester · Answer

$$y+3={-{\frac 1 2}} \times (x-4)$$
You can distribute the -(1/2) and subtract 3 from both sides to get your answer in point-slope form.
$$y+3={-{\frac 1 2}}x+2$$
$$y={-{\frac 1 2}}x-1$$

roadjester · Answer

I guess you could get a common denominator of 2.

anonymous · Answer

so it would be -1/2 because it is asking for the slope right?

roadjester · Answer

Pardon?

roadjester · Answer

You said you wanted the answer as a fraction, not the slope. The slope will obviously be a fraction.

roadjester · Answer

Never mind...extra information

anonymous · Answer

the question asked what is the slope of the line

roadjester · Answer

Right, sorry. I thought it wanted an equation. In that case, as I said earlier, an equation of a line has three forms. For a question like this, you want to first change it into point-slope form.

roadjester · Answer

oops, I mean y-intercept.

roadjester · Answer

In this case, you already have it in y-intercept form. The point given (4,-3) is extra information.

roadjester · Answer

You have a slope of 2 so $$\huge any$$ line with a slope of -1/2 will be perpendicular to the line given.

roadjester · Answer

That extra point is only if you're looking for a $$\large specific$$ line. My mistake sorry.

roadjester · Answer

Can I at least get a medal or do I not get one because I read the question incorrectly and basically wasted your time by going in circles? :)