Point Slope Form
y-y₁=m(x-x₁)
The point-slope form is one of the ways to represent a linear equation in algebra. It is used to specify a line’s equation using the slope of the line and a single point on that line. The point-slope form for a linear equation with a known slope (m) and a known point (x1, y1) is:
(y − y1) = m(x − x1)
This equation expresses the following: a line passes through the known point (x1, y1) and has the slope “m”. Using this equation, it is possible to find the equation of a line on a graph when certain information is known, such as a single point on the line and the slope of the line.
Here are some examples of how to use the point-slope form:
1. Find the equation of the line that passes through the point (2, 4) and has a slope of 3.
The point-slope form of a linear equation is (y − y1) = m(x − x1). Substituting the values we know
(y − 4) = 3(x − 2)
Expanding and simplifying the equation
y − 4 = 3x − 6
y = 3x − 2
Therefore, the equation of the line is y = 3x − 2.
2. Find the equation of the line passing through (1, 2) and (-3, 4).
The slope of the line can be calculated using the formula (y2 – y1) / (x2 – x1), where (x1, y1) = (1, 2) and (x2, y2) = (-3, 4).
Slope = (4 – 2) / (-3 – 1) = -1/2
Using one of the points and the slope, we can find the point-slope form
(y – 2) = -(1/2)(x – 1)
Expanding and simplifying the equation
y – 2 = -1/2 x + 1/2
y = -1/2 x + 5/2
Therefore, the equation of the line is y = -1/2 x + 5/2.
Overall, the point-slope form is a useful tool for calculating the equation of a line when given certain information, such as the slope and a point on the line.
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