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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. Line (geometry) - Wikipedia

   en.wikipedia.org/wiki/Line_(geometry)

   e. In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.

4. Parabola - Wikipedia

   en.wikipedia.org/wiki/Parabola

   The slope of the line BE is the quotient of the lengths of ED and BD, which is ⁠ x 2 / x/2 ⁠ = 2x. But 2x is also the slope (first derivative) of the parabola at E. Therefore, the line BE is the tangent to the parabola at E. The distances EF and EC are equal because E is on the parabola, F is the focus and C is on the directrix.

5. Parallel (geometry) - Wikipedia

   en.wikipedia.org/wiki/Parallel_(geometry)

   The binary relation between parallel lines is evidently a symmetric relation. According to Euclid's tenets, parallelism is not a reflexive relation and thus fails to be an equivalence relation. Nevertheless, in affine geometry a pencil of parallel lines is taken as an equivalence class in the set of lines where parallelism is an equivalence ...

6. Distance between two parallel lines - Wikipedia

   en.wikipedia.org/wiki/Distance_between_two...

   Given the equations of two non-vertical parallel lines. the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line. This distance can be found by first solving the linear systems. {\displaystyle {\begin {cases}y=mx+b_ {1}\\y=-x/m\,,\end {cases}}} and.

7. Linear equation - Wikipedia

   en.wikipedia.org/wiki/Linear_equation

   The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...

8. Line coordinates - Wikipedia

   en.wikipedia.org/wiki/Line_coordinates

   There are several possible ways to specify the position of a line in the plane. A simple way is by the pair (m, b) where the equation of the line is y = mx + b. Here m is the slope and b is the y -intercept. This system specifies coordinates for all lines that are not vertical. However, it is more common and simpler algebraically to use ...

9. Thales's theorem - Wikipedia

   en.wikipedia.org/wiki/Thales's_theorem

   In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements. [ 1]