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The answer will depend on the context.

If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.

Q: How do you get the tangent line without the graph?

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Tangent line is a graph. This graph is to gather data.

A tangent is a straight line which will intersect at another line only once. Every tangent for each point will be different, because each tangent is exclusive only to one point in a graph.

The gradient (slope) of the tangent to the graph at the given time - provided that it exists. If the graph is a straight line at that point, it is the gradient of that line.

Take a tangent at the point where you want the slope. Then the slope of the graph at that point is the slope of the tangent, which is found by taking another point on the tangent and then taking the change in y between the two points and divid it by the change in x.

That line is [ y = 2 cos(2x) ].

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Tangent line is a graph. This graph is to gather data.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

A tangent is a straight line which will intersect at another line only once. Every tangent for each point will be different, because each tangent is exclusive only to one point in a graph.

Yes, the derivative of an equation is the slope of a line tangent to the graph.

The gradient (slope) of the tangent to the graph at the given time - provided that it exists. If the graph is a straight line at that point, it is the gradient of that line.

Take a tangent at the point where you want the slope. Then the slope of the graph at that point is the slope of the tangent, which is found by taking another point on the tangent and then taking the change in y between the two points and divid it by the change in x.

That line is [ y = 2 cos(2x) ].

The rate of change on that line. This is called the tangent and is used in the application of the derivative.

When you graph a tangent function, the asymptotes represent x values 90 and 270.

y = e2 or e2 is not a function of x: it is a constant. So it is a horizontal straight line and its tangent, at any point, is itself.If you think I am going to sketch a graph on this browser, you have another think coming!y = e2 or e2 is not a function of x: it is a constant. So it is a horizontal straight line and its tangent, at any point, is itself.If you think I am going to sketch a graph on this browser, you have another think coming!y = e2 or e2 is not a function of x: it is a constant. So it is a horizontal straight line and its tangent, at any point, is itself.If you think I am going to sketch a graph on this browser, you have another think coming!y = e2 or e2 is not a function of x: it is a constant. So it is a horizontal straight line and its tangent, at any point, is itself.If you think I am going to sketch a graph on this browser, you have another think coming!

No. A tangent is a ratio without units. A line of 5 metres has a measurement unit: metres.

No, it is instantaneous acceleration.