Point-Slope Form – Calculation of Equation of a line

As you know that mathematics has two branches of algebra and geometry, in the concept of geometry, we study the point-slope form which is used to form the equation of a line which is formed straight, this is the slope that is inclined at a predetermined angle towards the X-axis and this passes through another point. The equation which forms the equation of the line is an equation that satisfies or proves each point. In order to calculate the equation of the line, these are the various methods that are in use:  

  • Slope-intercept form
  • Intercept form
  • Point slope form
  • Two-point form

These were the methods that are required in finding the equation of the lines. These methods are used based on different types of parameters.

When is the Point-Slope Formula Used?

The Point-Slope Formula is useful where the slope and the point on the line is known. In the question, the students will be given the slope determinant of the line and the specific point of the line with the coordinates placed on the graph. With these parameters, the students will need to find out the equation of the point-slope form.

What Do You Mean by Point-Slope Form?

The point-slope form is being defined as the straight line which is drawn using the slope and the point on the line. This means that an equation of the line with a distinct slope and passing through a point on this given line. Thus, the equation of the line will be y – y11 = m (x – x11). In this case, X and Y points are at many points on the line, while ‘m’ = slope of the line.

Tutor Hunt is a great resource for mastering the Point-Slope Formula, which is particularly useful when the slope and a point on the line are known. In this exercise, students will be given the slope determinant of the line and a specific point with coordinates placed on the graph.

What is Slope-Intercept Form?

After studying the point-slope form, now let’s study the slope-intercept form. Slope Intercept form is one of the most common forms which helps in representing an equation that lies in a straight line.

Use of Slope-Intercept Formula

In order to know the definition of the slope-intercept form, we must know about the uses of this form. The slope-intercept formula is applied when you are required to find the equation which is formed by the straight line. For this, we need to find the slope of the line and the intercept that is being cut by the line which is formed at the y-axis. If we consider p as the slope of the line and the y-intercept as d then, The slope-intercept form of the equation will be y = px + d

What is the Slope-Intercept Form in a Straight Line?

This is in fact the whole topic that is being discussed in this section. So, to sum up, the slope-intercept form is the method that is used to estimate the equation of a straight line that is located on a coordinate plane-like structure.

What is the Relation of the Equation with Other Determinants?  

The relation is numbered point-wise

  • the coordinates which are formed at any point on the line should necessarily satisfy the equation.
  • the coordinates of any point not on the line will not satisfy.

In order to determine the equation, the concept is pretty straight laid down. So, in order to find the slope of the intercept, we require to know the measure of the slope or the measure of the angle which is inclined to the straight line from the X-axis and this intercept will be made with the Y-axis at the point.

As we come to the end of the discussion about Point slope form and Slope intercept form, realise that learning this particular topic is much more beneficial with the graph paper, this will make our understanding clearer. The practice of this concept is required, by which the students will be shrewd enough to deal with any line equation. To know further on the topics, visit Cuemath.

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