Point Slope Form
y-y₁=m(x-x₁)
The point slope form is a linear equation that relates a line to a point on the line and the slope of the line. It is represented as:
y – y1 = m(x – x1)
where:
– (x1, y1) represents the given point on the line
– m is the slope of the line
This equation can be used to find the equation of a line when you know a point on the line and the slope, or to find the equation of a line given just two points on the line.
To use the point slope form, simply substitute the values of the given point and the slope into the equation, and then simplify the equation if possible.
For example, if you know the point (2, 5) is on a line with a slope of -3, you would substitute these values into the equation to get:
y – 5 = -3(x – 2)
Then, you can simplify the equation by distributing the -3:
y – 5 = -3x + 6
Lastly, you can solve for y by adding 5 to both sides:
y = -3x + 11
So the equation of the line that passes through the point (2, 5) with a slope of -3 can be written in point slope form as y – 5 = -3(x – 2), or in slope intercept form as y = -3x + 11.
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