Point Slope Form

About Point Slope Form

The point-slope form is used to obtain the equation of a straight line that passes through a given point and is inclined at a certain angle to the x-axis. A line's equation is a set of equations that are satisfied by every point on the line. This indicates that a two-variable linear equation represents a line. Depending on the information given, many methods can be used to find the equation of a line.

Some of the techniques include:

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

We use the point-slope formula when we know the slope of a line and a point on it. Let's go over the point-slope form and how to calculate the formula.

What is point-slope form?

A straight line is represented using its slope and a point on the line in point-slope form. For example, the point-slope form is used to find the equation of a line whose slope is 'm' and passes through a point (x1,y1). The equation of a straight line can be expressed in various ways. Point slope shape is one of them.

The point-slope form's equation is y-y1= m(x-x1)

The line's slope is m, and (x,y) is a random point on the line.

Point slope formula

To find the equation of a line, use the point-slope form formula. The point-slope form is used to find the equation of a line with a specified slope and a given point. This formula is only utilized when the slope of the line and a point on the line are both known. Other formulas for determining the equation of a line include slope-intercept form, intercept form, and so on. The point-slope formula is as follows:

Point slope formula in math???????

  • y-y1 = m(x-x1)
  • where,
  • (x, y) is a random point on the line(which should be kept as variables while applying the formula).
  • (x1,y1) is a fixed point on the line.
  • m is the slope of the line.

Derivation of point-slope formula

Let's look at how to calculate the point-slope form (i.e., the proof of the point-slope form formula). The slope of a line equation will be used to derive this expression.

Consider a line with the slope of'm.'

Assume (x1,y1) is a well-Known location on the line. Let (x,y) be any other random point on the line with unknown coordinates.

The slope of a line is calculated as Slope = (Difference in y-coordinates)/(Difference in x-coordinates)

point slope

  • m=(y-y1)/ (x-x1)
  • m(x-x1)=y-y1 by multiplying both sides by (x-x1)
  • which gives, y-y1=m(x-x1)
  • As a result, the point-slope formula is established.

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Point Slope Form
Point Slope Form

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