If a tangent line is inclined 45 degrees, then what is the slope the tangent line?

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Table of Contents Show

How to Use the Tangent Line Calculator?
What is Tangent?
Standard Equation

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Tangent line calculator is a free online tool that gives the slope and the equation of the tangent line. BYJU’S online tangent line calculator tool makes the calculations faster and easier where it displays the output in a fraction of seconds.

How to Use the Tangent Line Calculator?

The procedure to use the tangent line calculator is as follows:

Step 1: Enter the equation of the curve in the first input field and x value in the second input field

Step 2: Now click the button “Calculate” to get the output

Step 3: The slope value and the equation of the tangent line will be displayed in the new window

What is Tangent?

A tangent is a line that touches a curve at a point. The point where the curve and the line meet is called a point of tangency. The slope-intercept formula for a line is given by y = mx + b,

Where

m is the slope of the line

b is the y-intercept

Also, read: Slope of a line

Standard Equation

The standard form to find the equation of a tangent line is defined by

y – y1 = m (x – x1)

Where

(x1, y1) are the line coordinate points

m is the slope of the line

The point where the line and the curve meet is called the point of tangency.

The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

The tangent line to a circle is always perpendicular to the radius corresponding to the point of tangency.
The tangent always touches the circle at a single point.

Answer:

m = 1.62

Step-by-step explanation:

A TANGENT LINE is a line which "touches" a curve at a certain point.

Most of the lines are described by the GENERAL FORM FOR THE EQUATION OF THE LINE which is

Ax + By + C = 0

Where A, B, and C are real numbers

A SLOPE OF A LINE is the value which characterizes the direction at which the line goes. By also using the slope, we can determine the inclination of the line at an angle in degrees.

The formulas in solving for the slope of the line are

and

m = tan (Θ)

Where m is the slope of the line;

(x1,y1) as the first point

(x2,y2) as the second point

Θ as the angle of inclination

Since in the problem, we are given the angle by which the tangent line is inclined, we are to use the second formula.

Substituting the given values to the equation, we have

m = tan (Θ)

m = tan (45°)

By using the calculator, we have the value of m as