Interpolation Formula In the mathematical sub field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Linear interpolation is a method of curve fitting using linear polynomials. It is heavily employed in mathematics (particularly numerical analysis), and numerous applications including computer graphics. It is a simple form of interpolation. Many times, while making the graphs of functions in experimental science and statistical mathematics, we get such complex functions whose real set of coordinate points are difficult to obtain and plot on a graph. In such cases, we use the method of interpolation, and plot the graph of a simple function that has the closest graph to the original complex function. Although the graph of such a function is not accurate, the small error encountered by interpolation is negligible to the simplicity obtained in making complex graphs by interpolation. Linear Interpolation: Know More About Tutors Online For Free
The term "linear" in mathematics implies an equation whose degree is one. Thus, "linear interpolation" is the method of interpolation with linear functions and their graphs. Thus linear interpolation is the simplest type of interpolation. Definition of Linear Interpolation The linear interpolation is the straight line between the two points which are given by the coordinates (x0, y0) and (x1, y1). In the interval of (x0, x1) the value of x which gives the straight line and it is given from the equation for the value of y along. Example Problem for Linear Interpolation Formula: Some example problem for linear interpolation formula are, Example 1: Using linear interpolation formula, for the given coordinates of (1, 2) and (4, 5). Find the value for y when x = 2. Solution: Linear interpolation formula Learn More Free Math Tutors Online
y = y0 + (x- x0)y1−y0x1−x0 Given coordinate values are (1, 2) and (4, 5) (x0, y0) and (x1, y1) are (x0, y0) and (x1, y1). y = 2 +(x - 1) (5−2)(4−1) y = 2 + x -1 33 y = 2 + x - 1(1) y = x + 1. Value of y when x = 2. y=x+1 x=2 y = 2 +1 y = 3.
Define Parallel Lines Two lines are said to be parallel if they always maintain same distance apart. Parallel lines are also called as Equidistant. The parallel lines will never meet each other. Pair of Angles in Parallel Lines A line is called as the transversal, if it intersects two or more coplanar lines at a different point. Transversals tells us a great deal about the angles. Two lines are said to be parallel if they always maintain same distance apart. Parallel lines are also called as Equidistant. The parallel lines will never meet each other. A special rule that is used in geometry called as Transversal Postulate that involves angles and the transversals. The Transversal Postulate says that if two parallel lines are intersected by a line called transversal, then corresponding angles are congruent. When parallel lines are crossed by another line called as Transversal, we can notice that many angles will be same.
Properties of Parallel Lines If the pair of Corresponding Angles formed by two lines are equal, then the lines are called as Parallel Lines. The pair of consecutive angles of parallel lines add upto 180째 The pair of altenate interior angles of parallel lines are equal. Parallel Line Example Problems Below you could see some examples on parallel lines Example 1) Determine if y = 3x + 7 and -3x + y = -2 are parallel then graph the equations to check. Given lines are y = 3x + 7 and -3x + y = -2 Slope intercept form of the given lines is y = 3x + 7 --------------------> Slope =3 y = 3x - 2 --------------------> Slope =3 Since the slopes of the above two lines are equal, So the two lines are parallel. Read More About Free Tutors Online
Example 2) Determine if y =2x - 5 and -7x + y = 4 are parallel then graph the equations to check. Given lines are y =2x - 5 and -7x + y = 4 Slope intercept form of the given lines is y =2x - 5-----------------> Slope =2 y =7x + 4-----------------> Slope =7 Since the slopes of the above two lines are not equal, So the two lines are not parallel.