#### 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 parallel to coordinates?

Step 1: Find the slope of the line. To find the slope of the given 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 3x – 5y = 9 is m = 3/5. Therefore, the slope of the line parallel to this line would have to be m = 3/5.

## 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 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 .

## 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.

## 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.

## How do you put something into standard form?

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it’s pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

## How do you find the equation of a line with one point and parallel?

For parallel lines, the slopes must be equal, so the slope of the new line must also be . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line. Use the y-intercept in the slope-intercept equation to find the final answer.

## 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”.

## Is a tangent line perpendicular to the radius?

The radius of a circle is perpendicular to the tangent line through its endpoint on the circle’s circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line.