Point-slope form is a way to represent the equation of a straight line. It is called point-slope form because it uses the coordinates of a single point on the line and the slope of the line to determine the equation.
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The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where:
(x1, y1) is a point on the line
m is the slope of the line
To find the equation of a line in point-slope form given two points (x1, y1) and (x2, y2), we first need to calculate the slope m:
m = (y2 - y1) / (x2 - x1)
Then, we can plug in one of the points and the slope into the point-slope form to get the equation:
y - y1 = m(x - x1)
Alternatively, if we are given the slope m and a point (x1, y1), we can simply plug those values into the point-slope form to get the equation:
y - y1 = m(x - x1)
What is point slope form calculator?
A Point Slope Form Calculator is an online tool that helps you find the equation of a straight line in point-slope form. The point-slope form of a straight line is given by:
y – y1 = m(x – x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
The calculator requires you to input two pieces of information: the slope of the line and a point on the line. Here are the steps to use a Point Slope Form Calculator:
Step 1: Input the slope of the line
The first step is to input the slope of the line. This can be a fraction, decimal or whole number. Make sure that you enter the slope in the correct format, as indicated by the calculator.
Step 2: Input a point on the line
The next step is to input a point on the line. This is usually given in the form (x1, y1), where x1 and y1 are the coordinates of the point. You should enter these values in the appropriate fields provided by the calculator.
Step 3: Calculate the equation of the line
After inputting the slope and point on the line, click the “Calculate” or “Find Equation” button to generate the equation of the line in point-slope form.
Step 4: Interpret the result
The calculator will output the equation of the line in point-slope form. You can then interpret this equation to understand the characteristics of the line, such as its slope and y-intercept. You can also use the equation to graph the line or solve other related problems.
Overall, a Point Slope Form Calculator is a useful tool for quickly and accurately calculating the equation of a straight line in point-slope form.
Point slope formula
The point-slope formula is a method of writing the equation of a straight line in the form:
y – y1 = m(x – x1)
where (x1, y1) is a known point on the line, and m is the slope of the line.
This formula is used when you know a point on the line and its slope, and want to find the equation of the line. The formula can also be rearranged to solve for y, which gives the slope-intercept form of the equation:
y = mx – mx1 + y1
where m, x1, and y1 are known values.
To use the point-slope formula, you need to follow these steps:
Step 1: Identify a point on the line
Identify a point on the line that you want to find the equation for. The point should be in the form (x1, y1), where x1 and y1 are the coordinates of the point.
Step 2: Determine the slope of the line
Determine the slope of the line. This can be done by finding the change in y divided by the change in x between two points on the line, or by using other methods depending on the information you have.
Step 3: Substitute the values into the formula
Substitute the values of the known point (x1, y1) and the slope (m) into the point-slope formula:
y – y1 = m(x – x1)
Step 4: Simplify the equation
Simplify the equation by distributing the slope (m) and combining like terms. This will give you the equation of the line in point-slope form.
Alternatively, you can rearrange the point-slope formula to get the slope-intercept form of the equation:
y = mx – mx1 + y1
where m, x1, and y1 are known values.
How to find point slope form?
To find the point-slope form of a straight line, you need to follow these steps:
Step 1: Identify a point on the line
Identify a point on the line that you want to find the equation for. The point should be in the form (x1, y1), where x1 and y1 are the coordinates of the point.
Step 2: Determine the slope of the line
Determine the slope of the line. This can be done by finding the change in y divided by the change in x between two points on the line, or by using other methods depending on the information you have.
Step 3: Substitute the values into the formula
Substitute the values of the known point (x1, y1) and the slope (m) into the point-slope formula:
y – y1 = m(x – x1)
where (x1, y1) is the known point on the line, and m is the slope of the line.
Step 4: Simplify the equation
Simplify the equation by distributing the slope (m) and combining like terms. This will give you the equation of the line in point-slope form.
For example, suppose you want to find the point-slope form of a line that passes through the point (2, 3) and has a slope of 2. Using the point-slope formula, we can write:
y – 3 = 2(x – 2)
Expanding the right side and simplifying, we get:
y – 3 = 2x – 4
y = 2x – 1
Therefore, the point-slope form of the line is y – 3 = 2(x – 2), or alternatively, y = 2x – 1.