Normal form of a straight line

A normal to a line is considered as a line segment drawn from a point that is perpendicular to the given line. The normal form of a linear equation of a straight line uses two parameters: p and α to describe the line. Here, p stands for the length of the perpendicular from the origin … Read more

Slope intercept form of a straight line

An equation of a line can be written as a linear equation in slope-intercept form y = mx + b. Here, m is the slope and b is the y-intercept. The y-intercept is known as a point where a line crosses the y-axis. Example 1. Write an equation in slope-intercept form of the line that … Read more

Two intercept form of a straight line

We need at least two points to determine the nature of a line. This analogy is used to quickly sketch a line if its equation is given in the Two Intercept-Form. Consider the following graph where a line L makes x-intercept at a and y-intercept at b on the axes. This means that L meets … Read more

Point slope form of a straight line

Straight Lines: Equation of a line – point-slope form The slope-intercept form is simple to remember and use but it has one major disadvantage. We must know the y-intercept in order to use it. Generally, we do not know the y-intercept, we only know one or more points (that are not the y-intercept). In these … Read more

Straight Lines: 2D geometries

Figure 1: The coordinate plane. Cartesian coordinates In mathematics, a plane is defined as a flat infinite surface that spreads forever in every direction. In Algebra, we often use the coordinate plane which is divided by two number lines. The horizontal line is x-axis with negative points in the left of the origin and positive … Read more

Straight Lines: shifting of origin

Translation – The object is shifted on the plane without changing origin, axis or anything other than location. Translation type Rule Move right by a units Add a to each x-coordinate: (x,y) (x+a,y) Move left by a units Subtract a from each x-coordinate: (x,y) (x-a, y) Move up by b units Add b to each … Read more

Straight Lines: General equation of a line

Linear equations contain two variables and when we plot all the (x,y) pairs that make the equation for a line. The formula for Standard Form is: Here, A, B and C are real numbers and A≠ and B≠0. Since the slope of a vertical line is undefined we don’t write the equation of a vertical … Read more

Repeated independent (Bernoulli) trials and Binomial distribution

In order for an experiment to be called a Bernoulli trial, an experiment must meet each of three criteria: There must be only 2 possible outcomes, such as black or red, sweet or sour. One of these outcomes is called a success, and the other a failure. Successes and Failures are denoted as S and … Read more

Mean and variance of a random variable

The mean of a discrete random variable X can be explained as a weighted average of the possible values that the random variable contains. Contrary to the sample mean, which gives each observation equal weight, random variable mean weights each outcome xi as per its probability, pi. The commonly used symbol for the mean or expected value of X) is μ, and it is formally … Read more

Random variable and its probability distribution

A random variable is defined as a function that assigns a real number to each outcome in a sample space in the case of a random experiment. It is denoted by an uppercase letter, X while the measured value of the random variable is denoted by a lowercase letter, x. A discrete random variable lies … Read more