# MCQ Functions - Graphing Functions

The CAT Online Free Test Prep MCQs Functions - Graphing Functions

### Functions: Graphing Functions

#### Question: 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?

Option A:      $y=-\frac{3}{4}x+\frac{25}{2}$
Option B:      $y=\frac{3}{4}x+\frac{7}{2}$
Option C:      $y=-\frac{4}{3}x+16$
Option D:      Insufficient information is given to determine the equation of the line.
Option E:      $y=\frac{4}{3}x$

##### Explanation

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 $\left(6,8\right)$, we can use the point-slope form of the line to find its equation:

$y-{y}_{1}=m\left(x-{x}_{1}\right)$

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

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

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

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

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### How to Solve Graphing Functions

For Graphing Functions question first understand the statement and the question stem. Try to solve and click the corresponding answer option. The drop down will appear to show the correct answer and explanation.