# Tangent line through arbitrary point?

## Homework Statement

Consider the function f(x)=x2+5x+5 and the point A(4,5).

Find a formula for the slope of a line passing through point A, and an arbitrary point on the function. Your answer should be a formula in terms of x.
slope=???

f′(x)=2x+5

## The Attempt at a Solution

Using your answers from the two previous questions, find the slope(s) of the line(s) through point A that is (are) tangent to f(x)

the slopes are 1, and 25 however I don't understand what part two of the question is asking for...
(formula for slope passing through point A, and arbitrary point on the function)

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Mark44
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## Homework Statement

Consider the function f(x)=x2+5x+5 and the point A(4,5).

Find a formula for the slope of a line passing through point A, and an arbitrary point on the function. Your answer should be a formula in terms of x.
slope=???

f′(x)=2x+5

## The Attempt at a Solution

Using your answers from the two previous questions, find the slope(s) of the line(s) through point A that is (are) tangent to f(x)

the slopes are 1, and 25 however I don't understand what part two of the question is asking for...
(formula for slope passing through point A, and arbitrary point on the function)
First off, your thread title seems misleading to me, as this problem has nothing to do with tangent lines. All they are asking for is the slope of a line that goes through A(4, 5) and an arbitrary point on the graph of y = x2 + 4x + 5. Note that A is not on the graph of this parabola.

The question boils down to finding the slope of the line through two points: A(4, 5) and some point on the graph of the parabola. What are the coordinates of each point on the parabola?