Point Slope Formula For a Line
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The point-slope formula for a line is a method of representing the equation of a straight line in the Cartesian plane. It is called the point-slope formula because it requires only a single point on the line and the slope of the line to define the equation of the line. The formula is:
y – y₁ = m(x – x₁)
Where (x₁,y₁) is a point on the line, m is the slope of the line, and (x,y) is any other point on the line.
We can also rearrange the formula to the slope-intercept form, y = mx + b, by simplifying and solving for y, which results in:
y = mx + (y₁ – mx₁)
Where b = y₁ – mx₁ is the y-intercept of the line.
The formula is convenient for finding the equation of a line when the slope and a single point on the line are given. To use the formula, substitute the given values for x₁, y₁, and m into the equation and simplify to obtain the equation of the line in either point-slope form or slope-intercept form.
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