How do I find the slope of the line containing the two points (9,0) and (-5,6)
1 answer:
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Answer:
2,000 miles
Step-by-step explanation:
We are given:
This can be rewritten as:
This is representative of a unit rate, as we have a in the denominator. To calculate the number of miles in
inches, simply multiply the unit rate by
:
This can rewritten as:
Therefore, there are 2,000 miles in 4 inches.
-
We can check our solution by simplifying the fraction by dividing both
and
by
to see if we achieve the unit rate:
Since this is in fact the unit rate, our solution is correct!
First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
Which means that the roots are
Next, we can expand the function definition:
In this form, it is much easier to compute the derivative:
If we evaluate the derivative in the points of interest, we have
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
is what we need. The three lines are:
This is the tangent at x = -2
This is the tangent at x = 0
This is the tangent at x = 1