point slope form
The point-slope form is a way to express the equation of a straight line
The point-slope form is a way to express the equation of a straight line. It is given by the formula:
y – y₁ = m(x – x₁)
where (x₁, y₁) represents a point on the line, and m represents the slope of the line.
To understand how to use this form, let’s work through an example. Let’s say we are given a point (3, 5) and a slope of -2, and we want to find the equation of the line.
Using the point-slope form, we have:
y – 5 = -2(x – 3)
To find the equation in slope-intercept form (y = mx + b), we can simplify the equation:
y – 5 = -2x + 6
Next, we can isolate y by adding 5 to both sides of the equation:
y = -2x + 6 + 5
y = -2x + 11
Thus, the equation of the line in slope-intercept form is y = -2x + 11.
The point-slope form is particularly useful when you have a specific point and the slope of the line, as it allows you to easily write the equation.
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