# Questions tagged [slope]

For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.

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### Why does the limit give the exact value of the slope of the tangent?

This question has been already asked on this site many times but I haven't got a convincing answer and so some confusion lingers. Why limits give us the exact value of the slope of the tangent line? ...
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### Find the Slope of the Tangent line with First Principle Method

Given the function $y =\sqrt x-1$, determine the slope of the tangent when x = 10. You must find the slope of the tangent using the method first principles. I know how to find slope of a function but ...
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### How to make a 2-d linear function using a third variable for the iterator? [closed]

Say, for example, you have the vector $\vec {PQ} = \langle8,4\rangle$. As we all learned in Algebra I, the "traditional" slope (y-units per x-unit) would be $\frac{4}{8}$, and the slope for ...
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### Which rational slopes have angle bisectors with rational slopes?

This question was inspired by the following question in quora: The lines $y = 1/3 x$ and $y = 13/9 x$ are drawn in the coordinate plane. What is the slope of the line that bisects the angle these ...
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### Slope of secant and tangent lines (supported by MVT)

For the function $f(x) = x^{1/3}$ on the interval $[1,8]$ find the point $(c,f(c))$ guaranteed by the Mean Value Theorem, at which the slope of the tangent line is equal to the slope of the secant ...
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### If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines… find the value of $|A|$.

If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines with angle of intersection $'\theta'$ then find the value of |A|. I tried using general equation of ...
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### How do I determine if 3 points fall on a straight line?

$1.\;A(0,0,0),\,B(9,−4,3),\,C(−36,16,−12)\\ 2.\;D(9,−4,3),\,E(10,−2,6),\,F(14,6,18)\\ 3.\;G(−1,0,1),\,H(3,9,10),\,I(8,27,28)$ I want to determine if these points fall on a straight line. From my ...
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### How to find formula of line extruding from intersection point from two lines [closed]

wasn't exactly sure how to word this in a quick question title, but say I have the following: Meaning, I have two lines (or line segments) with known slopes and start / end verticies, and one ...
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### Intuition of product rule using graphs and slopes

I have seen formal proof of the product rule ($(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)$) and one with rectangles and areas - explanation seems reasonable. But, is there direct and intuitive proof using ...
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### Why does a kink sometimes ruin convexity of a set and other times not?

Specifically, I have the following in mind: Consider the positive quadrant as the domain (i.e. $(x,y)$ with $x,y\geq 0$). Consider a downward sloping line that divides this domain into two sets (the ...
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