Introduction to Point Slope Form Calculator:
Point Slope form Calculator is an online tool that helps you to find the straight line equation using the given slope point. It is used for the evaluation of algebraic equations using the coordinates geometry of the point slope form.
The point-slope form calculator is a beneficial tool for students, teachers, researchers or engineers to get the solution of the point slope problem easily and quickly without giving any external assistance.
What is Point Slope Form?
Point slope form is an algebraic process in which you find the equation of a straight line using the point slope formula in algebra. It is a useful method as it gives an equation line using cartesian coordinates at a specific point m.
The equation of a line is straight if it has no steepness that means if m = 0 then the given equation is at the x-axis on a graph. On the other hand for the vertical line, the point slope of the formula becomes undefined because of the decreased curve steepness.
Formula of Point Slope Form:
The formula of point slope form is the y coordinates with initial y1 values are equal to the slope of m with x coordinates and its initial value x1. The formula used by the Point slope form with two points calculator is,
$$ y - y_1 \;=\; m (x - x_1) $$
How to Calculate Point Slope Form?
To calculate the equation of a line using the point-slope form formula, you must follow these simple steps to get the straight line equation easily. Here is the calculation step of the Point Slope Form.
Step 1:
Identify the coordinates of a point (x0,y0) that lies on the line and the slope value m of the line.
Step 2:
The Formula of point slope form is,
$$ y - y_1 \;=\; m (x - x_1) $$
Step 3:
Substitute the given point values of x0, y0, and slope m in this formula.
Step 4:
After substitution, you can simplify the point slope form value equation for the solution of the equation of a straight line.
Practical Example Of Point Slope Form:
The practical example of point slope form with solution gives you conceptual clarity about the point slope form calculation.
Example: Find the equation of the line passing through points,
$$ P(-3,2)\; and\; Q(2,-1) $$
Solution:
The given cartesian coordinates is,
$$ P(-3,2)\; \; Q(2,-1) $$
To get the value of m use the below formula,
$$ m \;=\; \frac{\Delta y}{\Delta x} $$
Put these points in the above formula and solve it to get the value of m,
$$ m \;=\; \frac{\Delta y}{\Delta x} \;=\; \frac{-1 - 2}{2 - (-3)} \;=\; -\frac{3}{5} $$
$$ m \;=\; -\frac{3}{5} $$
The point slope form of equation line formula consists of coordinates point and m value,
$$ y - y_0 \;=\; m(x - x_0) $$
Put the given point value (x0,y0) and m value in it,
$$ m \;=\; - \frac{3}{5},\; x_0 \;=\; -3 \;and\; y_0 \;=\; 2 $$
$$ y - 2 \;=\; -\frac{3}{5}(x - (-3)) $$
Solve it to make a point slope equation,
$$ y - 2 \;=\; -\frac{3}{5}(x - (-3)) $$
$$ y - 2 \;=\; -\frac{3}{5}x - \frac{9}{5} $$
$$ 5(y - 2) \;=\; 5 \left(-\frac{3}{5}x - \frac{9}{5} \right) $$
$$ 5y - 10 \;=\; -3x - 9 $$
The equation of the point slope form of the straight line is,
$$ 3x + 5y \;=\; 1 $$
You can take the Q point as the value of x0 and y0 as you can get the same equation as you get from P point value.
How to Use Point Slope Form With Two Points Calculator?
Point Slope Form Calculator has a simple layout so that everyone can use it to solve point slope form line problems. You just need to put your coordinates value for the point-slope problem and follow some steps. These steps are:
- Enter the value of x0 and y0 value for the slope point form equation in the input field.
- Add the value of m which is the slope in the input field.
- Check the input slope point values that you provided before clicking the calculate button to get the solution in the point-slope form calculator.
- Click the “Calculate” button for the solution for the point-slope form problem.
- If you want to check the working process behind our point slope form to slope intercept form calculator, use the load example question to get an idea about its working method.
- Recalculate button provides you an opportunity to evaluate more examples of point slope form line questions to find the straight line.
Final Result of Point Slope Form.Calculator:
The points to point slope form calculatorprovides you with a solution equation of the line as per your input value of the slope line problem when you click on the calculate button. It may include:
- Result Option:
When you click on the result button, you get the solution of the point-slope form line problem.
- Possible Step Option:
Possible steps option gives you the solution of the point slope form value problem in a step-by-step method.
Advantages of Point Slope Form to Slope Intercept Form Calculator:
Point-slope form calculator has several advantages whenever you use it to solve point slope form problems and get its solution. These advantages are:
- Point slope form with two points calculator is a speedy tool that determines point slope form value problems with solutions in a couple of minutes without any external effort.
- It is an educational tool that helps children to learn the concept of the point slope form method for finding straight lines easily.
- Slope intercept form calculator with two points is a handy tool that quickly solves the point slope form problems with the help of its formula.
- It is a free tool that allows you to use it for calculating the equation of the line without any fee to get its solution.
- Point slope to standard form calculator has a user-friendly interface you do not need to become an expert for point slope form problems.
- Our Point Slope Form Calculator only takes the input value and provides a solution of the equation of line without sign-up condition.
