Point-slope formula
opposite reciprocal of slope of the tangent line
The point-slope formula is an equation used to find the equation of a straight line when we know the slope of the line and a point on the line. If we have a point(x₁,y₁) on the line and the slope of the line as m, then the point-slope formula is given as:
y – y₁ = m(x – x₁)
where y and x are the coordinates of any point on the line.
This formula can be used to find the equation of a line in both slope-intercept form and standard form.
To find the equation of a line in slope-intercept form, we can manipulate the point-slope formula by solving for y:
y – y₁ = m(x – x₁)
y = m(x – x₁) + y₁
y = mx – mx₁ + y₁
where m is the slope of the line.
To find the equation of a line in standard form, we can simplify the equation in slope-intercept form:
y = mx – mx₁ + y₁
mx – y = mx₁ – y₁
where m is the slope of the line, x and y are the variables, and x₁, y₁ are the coordinates of the given point.
The point-slope formula is a useful tool in finding the equation of a straight line, especially when we are given a point on the line and its slope.
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