Using coordinates and slope, the Point-Slope Form Calculator displays the equation of a line. With STUDYQUERIES’s online point-slope form calculator tool, calculations are made faster, and the graph of the point-slope form is displayed in a fraction of a second.

How to Use the Point-Slope Form Calculator?

To use the point-slope form calculator, follow these steps:

  • Step 1: Enter coordinates and slope in the input field
  • Step 2: Click the “Solve” button to get the equation
  • Step 3: In the output field, the equation of the line using the point and slope is displayed

Point-Slope Form Calculator


 

Disclaimer: This calculator is under development, so some of the inputs might not work. Sorry for the inconvenience.

Point Slope Form

The point-slope form is used to find the equation of the straight-line inclined at a given angle to the x-axis and passing through a given point. An equation of a line is an equation that is satisfied by each and every point on the line. Linear equations with two variables represent a line. According to the information available, a line’s equation can be found through a variety of methods. These are some of the methods:

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

When we know the slope of a line and a point on it, we can use the point-slope formula. In the following section, we will learn more about the point-slope form and how to derive the formula to represent it.

What is Point Slope Form?

The point-slope form is used to represent a straight line by using a point and its slope. The equation for a line whose slope is ‘m’ and which passes through a point (x1, y1) can then be found using the point-slope form. The equation of a straight line can be expressed in different ways. The point-slope form is one of them. The equation for the point-slope form is:

y – y1 = m(x – x1)

The point (x, y) is randomly chosen along the line, and m is its slope.

Point Slope Formula

You can find the equation of a line using the point-slope form formula. A line’s equation will be found using the point-slope form if a slope is given and a point is given. Using this formula, we can determine the slope and the point on the line only if we know the slope and the point along the line. For example, slope-intercept form, intercept form, etc., can also be used to determine a line’s equation. The formula for slope-points 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 treated like variables when applying the formula).
  • (x1, y1) is a fixed point on the line.
  • m is the slope of the line.

Derivation of Point-Slope Formula

The proof of the formula for the point-slope form can be found by using the point-slope form (i.e. the proof). We will derive this formula from the equation for the slope of a line. Consider a line with a slope of m. The position of (x1, y1) on the line is known. Let (x, y) be any other random point on the line whose coordinates are unknown.

Point-Slope Form Calculator
Point-Slope Form Calculator

We know that the equation for the slope of a line is:

Slope = (Difference in y-coordinates)/(Difference in x-coordinates)

m = (y – y1)/(x – x1)

Multiplying both sides by (x – x1),

m(x – x1) = y – y1

This can be written as,

y – y1 = m(x – x1)

Hence the point-slope formula is proved.

Point Slope Formula Examples

The following examples demonstrate how the point-slope form formula works.

  • The equation of a line with slope (-1) and a point (1, 2) is found using: y – 2 = (-1)(x – 1).
  • The equation of a line with slope (3/2) and a point (-1/2, 2/3) is found using: y – (2/3) = (3/2) (x – (-1/2)).
  • The equation of a line with slope (0) and a point (3, -2) is found using: y – (-2) = 0(x – 3).

In each of these cases, we can simplify the equation further and get it to the form: y = mx + b.

Important notes on Point-Slope Form

  • The equation of the point-slope form of a line whose slope is ‘m’ and that passes through a point (x1, y1) is y – y1 = m(x – x1).
  • A horizontal line passing through (a, b) has the equation y = b.
  • A vertical line passing through (a, b) has the equation x = a.

This is an exceptional case when the point-slope form cannot be used.

How to Solve Point-Slope Form?

We can follow the steps given below to solve the point-slope form for a straight line in order to find its equation.

  • Step 1: Note down the slope, ‘m’ of the straight line, and the coordinates(x1, y1) of the given point that lies on the line.
  • Step 2: Substitute the given values in the point-slope formula: y – y1 = m(x – x1).
  • Step 3: Simplify to obtain the equation of the line in standard form.

Let us see an example to understand the application of the above steps on the point-slope form.

Example: Find the equation of a line that passes through a point (2, -3) and whose slope is (-1/2).

Solution: The point on the given line is: (x1, y1) = (2, -3)

The slope of the line is: m = (-1/2)

The equation of the line is found using the point slope form:

y − y11 = m(x − x11)

y − (−3) = (−1/2)(x − 2)

y + 3 = (−1/2)x + 1

Subtracting 3 from both sides,

y = (−1/2)x − 2

Thus, the equation of the required line is, y = (−1/2)x − 2.

Frequently Asked Questions About Point Slope Form Calculator

How do you write an equation in point-slope form?

For a point in space, the equation is y – y1 = m(x – x1). Here, x1, y1 represent coordinates of the point, and The slope is given by m.

Is Point slope form the same as Y MX B?

If you are familiar with slope-intercept equations, then you know the y=mx+b form (or slope-intercept equation of a line). The equation is the same but in a different format! The “b” value (also known as the y-intercept) indicates where the line crosses the y-axis.

What is meant by point-slope form?

The equation of a straight line in the form y − y1 = m(x − x1), where m is the slope of the line and (x1, y1) are the coordinates of a point on the line.

What is the slope formula for 2 points?

You can find the slope of a line given the coordinates of two points on the line using the slope formula. The slope is calculated by multiplying the change in y values by the change in x values, m=(y2-y1)/(x2-x1). x1 and y1 are the coordinates of the first point. The second point’s coordinates are x2, y2.

What does a slope-intercept equation look like?

Y = mx + b gives the slope-intercept equation for a straight line with a slope, ‘m’, and ‘b’ as the y-intercept.