BASIC COLLEGE ALGEBRA
BASIC COLLEGE ALGEBRA MAC 1105
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This 10 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1105 at University of Florida taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/207049/mac-1105-university-of-florida in Calculus and Pre Calculus at University of Florida.
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Date Created: 09/19/15
L 1 1 Circles Lines Circle A circle is the set of all points in the xyplane Which are a xed distance r radius from a xed point hk center 0fthe circle 1 2 73 4 5 The standard form of an equation of a circle With radius r and center hk is xih2 y7k2 r2 The standard form With center at the origin The equation of the Unit Circle The general form of the equation of a circle Example Describe the graph of x2 y2 8 Example Graph the equation x 32 y42 25 9 a 7 s 5 A 3 2 1 1 2 3 A 5 s 7 a 9 Example Find the standard form of the equation of the circle with 1 center at the point 52 and radius 6 2 center at the point 4 6 and passing through the point 12 102 3 endpoints of a diameter at 24 and 4 6 Rewrite the last equation in general form 103 Example Write the equation in standard form If the equation represents a circle identify its center and radius Find the intercepts if any Graph the equation 9x2 9yZ 12x76y 4 0 Lines Slope ofa Line The slope m of a nonvertical line L is a quotient of the change in y Rise over the change in x Ran that is mRiseampyZ y1 Ran Ax xZ x1 where x1 ylx2y2are any two distinct points on the line The slope of a vertical line is unde ned Note If Run 1 then Rise 2 in slope Example Find the slope of the line whose graph is given below 105 Example Find the slope of the line passing through the points 62 and 5 4 2725 and J75 3 2 and 35 Note 1 A line with a positive slope rises from left to right 2 A line with a negative slope falls from left to right 3 A line with a zero slope is horizontal 4 A line with undefined slope is vertical Example Draw the line that has slope 3 and passes through the point l4 Equations of Lines The vertical line passing through the point ab has an equation x a where a is also the xintercept PointSlope Form of an Equation of a Line The line with the slope m passing through the point x1y1 has an equation yy1mxx1 The horizontal line passing through the point ab has an equation y b where b is also the yintercept 107 Exalnple Find an equation of the line passing through 35 With the slope m 2 Exalnple Find an equation of the line passing through 64 and 4 2 Exalnple Find an equation of the line Which is vertical With the xintercept 3 5 horizontal containing the point 32 SlopeIntercept Fonn of the Equation of a Line The line with the slope m and yintercept b has an equation ymxb Example Find the slope m and yintercept b of the line with the equation 3x y 2 Graph the equation 1 2 73 4 5 Example Find an equation of the line containing the points 2 2 and 3 4 WIite the final answer in the slopeintercept fonn An equation of a line is in general form if it is written as Ax By 2 C where A B and C are real numbers and A and B are not both equal to O Intercept Form of the Equation of a Line An equation of the line with the xintercept a and y intercept b 01 72 O is i Z 1 a b Example Find an equation of the line with the xintercept 3 and yintercept 4 110
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