# How do you find the equation of a line tangent to #y=4-3x# at (1,1)?

See below.

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To find the equation of a line tangent to a curve at a given point, we need to determine the slope of the curve at that point. In this case, the given curve is y = 4 - 3x and the point of tangency is (1,1).

To find the slope of the curve at (1,1), we can take the derivative of the equation y = 4 - 3x with respect to x. The derivative of -3x is -3, as the derivative of a constant multiplied by x is the constant itself.

Therefore, the slope of the curve at any point is -3.

Since the line tangent to a curve at a given point has the same slope as the curve at that point, the equation of the tangent line is y - 1 = -3(x - 1).

Simplifying this equation, we get y - 1 = -3x + 3.

Rearranging the terms, the equation of the line tangent to y = 4 - 3x at (1,1) is y = -3x + 4.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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