Point Slope Form
y-y₁=m(x-x₁)
The point slope form is a way to represent the equation of a line in algebraic form. This form is useful when we have a point (x1, y1) on the line and the slope (m) of the line. The point slope form of a line is given as:
y – y1 = m(x – x1)
where (x1, y1) is the known point, m is the slope of the line and x and y are the variables of the equation.
To use the point slope form, we need to find the values of m and (x1, y1). We can do this by using the given information such as the coordinates of a point and the slope of the line or using two given points on the line to determine the slope.
For example, let’s say we are given a point (3, 5) on a line with a slope of 2. To write the equation of the line in point slope form, we can substitute the values of (x1, y1) and m into the equation as follows:
y – 5 = 2(x – 3)
We can simplify this equation by distributing 2 to (x – 3) and adding 5 to both sides:
y = 2x – 1
Therefore, the equation of the line in point slope form is y – 5 = 2(x – 3) or y = 2x – 1.
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