SAT II Math II : Graphing Linear Functions

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #72 : Functions And Graphs


Note: Figure NOT drawn to scale.

Refer to the above figure. The circle has its center at the origin; the line is tangent to the circle at the point indicated. What is the equation of the line in slope-intercept form?

Possible Answers:

Insufficient information is given to determine the equation of the line.

Correct answer:


A line tangent to a circle at a given point is perpendicular to the radius from the center to that point. That radius, which has endpoints ,  has slope


The line, being perpendicular to this radius, will have slope equal to the opposite of the reciprocal of that of the radius. This slope will be . Since it includes point , we can use the point-slope form of the line to find its equation:


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