Understanding the Point-Slope Form of a Linear Equation and Its Applications.

Point Slope Form

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

The point-slope form is a linear equation form that represents a straight line. It is written as:

y – y₁ = m(x – x₁)

Where:
– y and x are the coordinates of any point on the line (x, y).
– y₁ and x₁ are the coordinates of a specific point on the line, often referred to as the “point-slope” or “base” point.
– m represents the slope of the line.

To use the point-slope form, you need to know the coordinates of a point on the line and the slope.

Let’s say we have a line with a slope of 2 and a point on the line is (3, 4). We can write the equation of the line using the point-slope form as:

y – 4 = 2(x – 3)

To find the equation of the line in slope-intercept form, we can simplify this equation:

y – 4 = 2x – 6
y = 2x – 6 + 4
y = 2x – 2

So, the equation of the line with a slope of 2 passing through the point (3, 4) is y = 2x – 2.

The point-slope form is particularly useful when you have a specific point and the slope of a line, as it allows for a straightforward conversion to other linear equation forms, such as slope-intercept form (y = mx + b). It provides a way to express the characteristics of a line in a concise and efficient manner.

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