ACT Math : How to find the slope of a tangent line
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Example Questions
Example Question #1 : How To Find The Slope Of A Tangent Line
. At this point meets a tangent line, which also passes through the point 
. What is the slope of the line perpindicular to this tangent line?
In this kind of problem, it's important to keep track of information given about your line of interest. In this case, the coordinates given set up the stage for us to be able to get to our line of focus - the line perpendicular to the tangent line. In order to determine the perpendicular line's slope, the tangent line's slope must be calculated. Keeping in mind that:
where y2,x2 and y1,x1 are assigned arbitrarily as long as the order of assignment is maintained.
To calculate the perpendicular line, we have to remember that the product of the tangent slope and the perpendicular slope will equal -1.
Example Question #1 : Coordinate Plane
Find the slope of the tangent line to 
To find the slope of the tangent line, we must take the derivative.
By using the Power Rule we will be able to find the derivative:
Therefore derivative of 
Now we plug in 
Example Question #1 : How To Find The Slope Of A Tangent Line
A line runs tangent to a circle at the point 
Cannot be determined
The only two bits of information that are given for the tangent line is that it runs through the points 
where 
Slope can be calculated through substituting in for the given values:
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