Graphing Functions

Solve the question of Graphing Functions and select the option from the choices A through D/E. Check your Answer and view the explanation.

Question: 1

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?

$y = - \frac{3}{4} x + \frac{25}{2}$
$y = \frac{3}{4} x + \frac{7}{2}$
$y = - \frac{4}{3} x + 16$
Insufficient information is given to determine the equation of the line.
$y = \frac{4}{3} x$

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Correct Answer: A

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 (0,0),(6,8), has slope

$m = \frac{8 - 0}{6 - 0} = \frac{8}{6} = \frac{4}{3}$

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 $- \frac{3}{4}$ . Since it includes point $(6, 8)$ , we can use the point-slope form of the line to find its equation:

$y - y_{1} = m (x - x_{1})$

$y - 8 = - \frac{3}{4} (x - 6)$

$y - 8 = - \frac{3}{4} x + \frac{9}{2}$

$y - 8 + 8 = - \frac{3}{4} x + \frac{9}{2} + 8$

$y = - \frac{3}{4} x + \frac{25}{2}$

Graphing Functions

Question: 1

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Correct Answer: A

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