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  2. Slope - Wikipedia

    en.wikipedia.org/wiki/Slope

    Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

  3. Slope field - Wikipedia

    en.wikipedia.org/wiki/Slope_field

    The slope field can be defined for the following type of differential equations ′ = (,), which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution (integral curve) at each point (x, y) as a function of the point coordinates. [3]

  4. Partial derivative - Wikipedia

    en.wikipedia.org/wiki/Partial_derivative

    To find the slope of the line tangent to the function at P(1, 1) and parallel to the xz-plane, we treat y as a constant. The graph and this plane are shown on the right. Below, we see how the function looks on the plane y = 1. By finding the derivative of the equation while assuming that y is a constant, we find that the slope of f at the point ...

  5. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...

  6. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them. There are several ways to write a linear equation of this line. If x 1 ≠ x 2, the slope of the line is . Thus, a point-slope form is [3]

  7. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The ratio in the definition of the derivative is the slope of the line through two points on the graph of the function ⁠ ⁠, specifically the points (, ()) and (+, (+)). As h {\displaystyle h} is made smaller, these points grow closer together, and the slope of this line approaches the limiting value, the slope of the tangent to the graph of ...

  8. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.

  9. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    If x kilograms of salami and y kilograms of sausage costs a total of €12 then, €6×x + €3×y = €12. Solving for y gives the point-slope form y = − 2 x + 4 {\displaystyle y=-2x+4} , as above.