The slope-intercept form is often written as y = mx + b.DespicableMe said:Homework Statement
What is the equation of the tangent line to the curve y = Sqrt( 2x - 1) where the tangent line is parallel to the line x - 3y = 16
The Attempt at a Solution
My teacher briefly mentioned to find the derivative of the given, and then plug it into the slope-y intercept formula? I got confused from there because he used y-y=m(x-x)
A tangent line is a line that touches a curve or surface at a single point and has the same slope as the curve or surface at that point.
To find the equation of a tangent line, you will need to know the slope of the tangent line and the coordinates of the point where it touches the curve. You can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the point.
The slope of a tangent line can be found by taking the derivative of the function at the point where the tangent line touches the curve. This derivative represents the slope of the tangent line at that point.
No, a tangent line can only touch a curve at one point. If a line intersects a curve at more than one point, it is not a tangent line.
A secant line is a line that intersects a curve at two or more points, while a tangent line only touches the curve at one point. Additionally, the slope of a secant line is an average of the slopes of the curve at the two points of intersection, while the slope of a tangent line is the slope of the curve at the point of tangency.