#### Find an equation of the line that is tangent to the graph of f and parallel to the given line

## How do you find the equation of a line that is tangent to a perpendicular line?

Answer: The line perpendicular to the curve at (2,1) will have slope equal to the negative reciprocal of the slope of the tangent line. Therefore, we should first determine the slope of the tangent line, which is given by the derivative of the function at the point. For any x, y (x)=3×2 – 4. y (2) = 3(2)2 – 4=8.

## How do you find the equation of a tangent line?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

## How do you find parallel lines?

Two lines are parallel if the have the same slope. Example 1: Find the slope of the line parallel to the line 4x – 5y = 12. To find the slope of this line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the line 4x – 5y = 12 is m = 4/5.

## How do you find the equation of a line?

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

## How do you find the tangent line to a curve?

In order to find the equation of a tangent, we:Differentiate the equation of the curve.Substitute the value into the differentiated equation to find the gradient.Substitute the value into the original equation of the curve to find the y-coordinate.Substitute your point on the line and the gradient into.

## How do you find the horizontal tangent?

To find the points at which the tangent line is horizontal, we have to find where the slope of the function is 0 because a horizontal line’s slope is 0. That’s your derivative. Now set it equal to 0 and solve for x to find the x values at which the tangent line is horizontal to given function.

## Do parallel lines have the same slope?

In other words, the slopes of parallel lines are equal. Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.

## What does it mean when a line is tangent to another line?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. The word “tangent” comes from the Latin tangere, “to touch”.

## How do I find the slope of the line?

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .