Question

1. # Find Equations Of The Tangent Lines To The Curve Y=(X-1)/(X+1) That Are Parallel To The Line X-2Y=4

Finding equations of tangent lines to a curve can often be a challenging task. Fortunately, with the right knowledge and understanding of calculus, it is possible to find equations for tangent lines that are parallel to specific lines. In this blog post, we will explore how to find equations for the tangent lines to the curve y=(x-1)/(x+1) that are parallel to the line x-2y=4. We’ll look at what these equations mean and how they can be used in various situations. So if you’re ready, let’s get started!

## What is the equation of the tangent line to the curve y=(x-1)/(x+1) that is parallel to the line x-2y=4?

The equation of a tangent line to the curve y=(x-1)/(x+1) that is parallel to the line x-2y=4 can be found using the following steps:

1. Find the slope of the curve at the point where the tangent line intersects it. This can be done by taking the derivative of y=(x-1)/(x+1).

2. Find the slope of the line x-2y=4.

3. Set the slopes equal to each other and solve for y. This will give you the equation of the tangent line.

## How do you find equations of tangent lines?

To find the equation of the tangent line to the curve y=(x-)/(x+) that is parallel to the line x-y=, we use the following steps:

1. We first find the slope of the curve at the point where we want to find the equation of the tangent line. To do this, we take the derivative of y with respect to x:

2. Next, we plug in the coordinates of the point where we want to find the equation of the tangent line into our formula for slope:

3. Now that we have our slope, we can use it to write down an equation for our desired tangent line using any point on that line:

4. Finally, we solve for y in our equation to get our final answer:

## What is the slope of the tangent line to the curve y=(x-1)/(x+1) at the point (2, -1)?

At the point (2, -1), the slope of the tangent line to the curve y=(x-1)/(x+1) is -2. This can be calculated using the formula for the derivative of a function:

dy/dx = (x+1)^(-2)*(1-2*(x-1))/(x+1)^2

Plugging in x=2, we get dy/dx = -2. This means that the equation of the tangent line at this point is y=-2*x+3.

## How do you find the equation of a line given its slope and

To find the equation of a line given its slope and a point on the line, we can use the point-slope form of a line. This form is:

y – y1 = m(x – x1)

where m is the slope and (x1, y1) is a point on the line. We can plug in our values for m and (x1, y1) to get our equation.

2. Are you stumped trying to find the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y = 4?

Don’t worry, we’ve got you covered! In this blog post, we’ll walk you through the steps to find the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y = 4.

To begin, let’s start by reviewing some key concepts. First, we must understand what a tangent line is. A tangent line is a line that intersects a curve at one point and is parallel to the curve at that point.

Now let’s talk about the equation of the line we’re trying to find. We know that the equation of the line we’re trying to find is parallel to the line x-2y = 4. This means that the slope of the line we’re looking for is the same as the slope of the line x-2y = 4. To find the slope of the line x-2y = 4, we must use the slope-intercept form of the equation, which is y = mx + b. Let’s plug in the values of the equation x-2y = 4 into the slope-intercept formula to get y = -1/2x + 2. Therefore, the slope of the line x-2y = 4 is -1/2.

Now that we know the slope of the line we’re looking for, let’s move on to finding the equation of the curve y = (x-1)/(x+1). To do this, we must first find the slope of the curve. To find the slope of the curve, we must use the derivative of the equation. The derivative of the equation y = (x-1)/(x+1) is dy/dx = 1/(x+1)².

Now that we know the slope of the curve and the slope of our line, we can begin to find the equations for the tangent lines. To find the equation of the tangent line, we must use the point-slope form of the equation, which is y – y1 = m(x-x1). Let’s plug in the values of the slope and the point from the curve y = (x-1)/(x+1) into the point-slope formula. The point from the curve y = (x-1)/(x+1) is (1, 0). Plugging in the values of the slope and the point from the curve y = (x-1)/(x+1), we get y – 0 = 1/(x+1)² (x-1). Rearranging the equation, we find that the equation of the tangent line is y = 1/(x+1)² + 1.

Now let’s find the equation of the other tangent line. To do this, we must use the same point-slope formula, but with the slope of the line x-2y = 4, which is -1/2. Plugging in the values of the slope and the point from the curve y = (x-1)/(x+1) into the point-slope formula, we get y – 0 = -1/2(x-1). Rearranging the equation, we find that the equation of the other tangent line is y = -1/2x + 1.

Congratulations! You have successfully found the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y = 4.