Point slope form calculator will give the equation of line in the general form. This line passes through the point A and has the slope m. Input: An ordered pair of real numbers or variables as coordinates of a point and a real number or variable as coefficient of a slope. Output: An equation of a line in the general form, Ax + By + C = 0. What is a slope? The word “slope” in math has roughly the same meaning in math as it has in.

Point of Intersection Formula

Have you heard of point of intersection concept in mathematics? If no, don’t panic. Here, we will discuss the point of intersection in detail and how to calculate it either graphically or algebraically. Also, the formula is applicable to a variety of areas like businesses, finance, study, construction, or physics etc.

Have you ever noticed the traffic signal on a road? This is the example of point of intersection that will appear at the point when two roads are meeting up at a point. In mathematics, point of intersection is the point where two lines or curves generally meet.The value of two curves would be same significantly and it can be used at multiple places.

Take another example, if we wanted to represent the revenue of a Company against the costs then point of intersection would define the situation where revenue and costs are significantly the same. Most of the times, this is the breakeven point for a Company. The point can be calculated either graphically or algebraically.

Draw the graph of two equations and see where they will intersect visually. This is not a tough job but can be completed quickly with a deep understanding and practice. In most of the examples, you could analyze that graph is the best technique to find the point of intersection with accuracy.

Pt Slope Formula Physics

Sometimes, there are the situation when this is not possible to find the point of intersection graphically then how can you solve the equation. The answer is you can do it algebraically. Solve the equations find the values of x coordinated that would point of intersection for both the equations.

Point Gradient Formula

For a line, the ratio of vertical change to the horizontal change is defined through a point i.e. named as the point of gradient or we can name it as the derivative as well. In brief, the gradient of a line will be rise divided by the run – rise/run. If m is the gradient point across a line then point gradient formula in mathematics could be given as –

[large Point;Gradient =frac{y-y_{1}}{x-x_{1}}]

Point Slope Form Formula

The other popular format for straight line equations is point slope formula. For this purpose, you need to find out the values (x1, y1) and a slope m. Further, plug the values into the formula –

[large y-y_{1}=m(x-x_{1})]

Where,
m is the slope of the line.
x₁ is the co-ordinates of x-axis.
y₁ is the co-ordinates of y-axis.

Don’t scare of subscripts but they are just intended to indicate the points given to you. If you have the generic values for x and y coordinates then it can be directly plugged into the formula to calculate the final output. If you will calculate the values calculated from the slope-intercept form and the point slope form then they are exactly the same.

So, this is your choice which method are you planning to use and which technique suits you the most. Practice the technique and apply it as per your convenience for next mathematics problem.

Video Tutorial

on Finding the Equation of a line From 2 points

Slope intercept vs Point Slope Form

There are a few different ways to find the equation of line from 2 points.

The first half of this page will focus on writing the equation in slope intercept form like example 1 below.

However, if you are comfortable using the point slope form of a line, then skip to the second part of this page because writing the equation from 2 points is easier with point slope form .

Example

Equation from 2 points using Slope Intercept Form

Find the equation of a line through the points (3,7) and (5,11)

Substitute the slope for 'm' in the slope intercept form of the equation

Substitute either point into the equation. You can use either (3,7) or (5,11)

Use our Calculator

You can use the calculator below to find the equation of a line from any two points. Just type numbers into the boxes below and the calculator (which has its own page here) will automatically calculate the equation of line in point slope and slope intercept forms

( Try this 'equation from 2 points' calculator on its own page here . )

Practice Problems

Substitute the slope for 'm' in the slope intercept form of the equation

Substitute either point into the equation. You can use either (4,5) or (8,7)

Substitute the slope for 'm' in the slope intercept equation

Substitute either point into the equation. You can use either (-6,7) or (-9,8)

$$ y = frac{1}{3}x +red{b} y = frac{1}{3}x +red{5} $$

Substitute the slope for 'm' in the slope intercept equation

Substitute either point into the equation. You can use either (-3,6) or (15,-6)

Example 2

Equation from 2 points using Point Slope Form

As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope.

The main advantage, in this case, is that you do not have to solve for 'b' like you do with slope intercept from.

Find the equation of a line through the points (3,7) and (5,11)

Calculate the slope from the 2 points

Substitute the slope for 'm' in the point slope equation

y − y₁ = m(x −x₁)
y − y₁ = 2(x −x₁)

Substitute either point as x1, y1 in the equation. You can use either (3,7) or (5,11)

using (3,7):
y − 7 = 2(x− 3)

using (5,11):
y − 11 = 2(x − 5)

Practice Problems

Substitute the slope for 'm' in the point slope equation

Substitute either point into the equation. You can use either (4,5) or (8,7)

using (4,5):
y − 5 = ½(x − 4)

using (5,11) :
y − 11 = ½(x − 5)

Substitute the slope for 'm' in the point slope equation

Pt Slope Formula Example

Substitute either point into the equation. You can use either (-6,7) or (-9,8)

using (-6,7):
y − 7 = (x + 6)

using (-9, 8):
y − 8 = (x +9)

Substitute the slope for 'm' in the point slope equation

Point Slope Formula Calculator

Substitute either point into the equation -3,6) and (15,-6)

using (-3, 6):
y − 6 = (x + 3)

using (15, -6):
y + 6 = (x − 15 )

If you read this whole page and looked at both methods (slope intercept form and point slope, you can see that it's substantially quicker to find the equation of line through 2 points by means of point slope

Point Slope Formula Equation

Linear Equations: