Point-Slope Form | How to Represent a Straight Line with One Point and the Slope

point slope

The point-slope form is a linear equation that represents a straight line on a coordinate plane

The point-slope form is a linear equation that represents a straight line on a coordinate plane. It is named “point-slope” because it requires one point on the line and the slope of the line.

The point-slope form equation is represented as follows:
y – y₁ = m(x – x₁)

In this equation, (x₁, y₁) represents the coordinates of a point on the line, and ‘m’ represents the slope of the line.

To use the point-slope form, you need to know a point on the line and its slope. Once you have these values, you can substitute them into the equation to find the equation of the line.

For example, let’s say we have a point (2, 4) on a line with a slope of -3. We can substitute these values into the point-slope form equation:

y – 4 = -3(x – 2)

Next, we can simplify the equation by distributing the -3 to the terms inside the parentheses:

y – 4 = -3x + 6

Finally, we can rearrange the equation to get it in the standard form (y = mx + b):

y = -3x + 10

So, the equation of the line with a point (2, 4) and a slope of -3 is y = -3x + 10.

The point-slope form is particularly useful when you have a specific point on a line and want to find the equation of that line. It provides a concise and efficient way to represent the relationship between the coordinates of a point and the slope of a line.

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