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 Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exponents Percentages Proportional reasoning Radical expressions Graphs Algebra Monomials Polynomials Factoring Linear Equations Graphs of linear equations Rectangular Coordinate System Midpoint Formula Definition of Slope Positive and negative slope Determine the slope of a line Equations of lines Equation of lines (from graph) Applications of linear equations Inequalities Quadratic equations Graphs of quadratic equations Absolute Value Radical expressions Exponential equations Logarithmic equations System of equations Graphs and functions Plotting points and naming quadrants Interpreting Graphs Relations and Functions Function Notation Writing a Linear Equation from a Table Writing a Linear Equation to describe a Graph Direct Variation Indirect Variation Domain and range Sequences and series Matrices Inverse of a matrix Determinants Inner product Geometry Triangles Polygons 2-D Shapes 3-D Shapes Areas Volume Pythagorean Theorem Angles Building Blocks Geometry Transformations Parallel, coincident and intersepting lines Distances in the plane Lines in space Plane in space Angles in the space Distances in the space Similarity Precalculus Sequences and series Graphs Graphs Definition of slope Positive or negative slope Determine the slope of a line Equation of a line (slope-intercept form) Equation of a line (point slope form) Equation of a line from graph Domain and range Quadratic function Limits (approaches a constant) Limits (approaches infinity) Asymptotes Continuity and discontinuities Parallel, coincident and intersepting lines Introduction to Functions Limits Continuity Asymptotes Trigonometry Trigonometric ratios The reciprocal trigonometric ratios Trigonometric ratios of related angles Trigonometric identities Solving right angles Law of sines Law of cosines Domain of trigonometric functions Statistics Mean Median Mode Quartiles Deciles Percentiles Mean deviation Variance Standard Deviation Coefficient of variation Skewness kurtosis Frequency distribution Graphing statistics & Data Factorial Variations without repetition Variations with repetition Permutations without repetition Permutation with repetition Circular permutation Binomial coefficient Combinations without repetition Combinations with repetition

 Graphs and Functions Direct Variation The quantity y is directly proportional to a quantity x if y=kx, where k is a constant, called the constant of variation. Given that p varies directly as q, find an expression for p in terms of q if p=126 when q=7. 1. Since p varies directly as q, write p=kq 2. Since p=126 when q=7, substitute these values to obtain 126=k(7), or k=18. 3. Hence p=18q is the required expression. y varies directly as the cube of x. If y=32 when x=2, find y when x=3. y=kx3 32=k(2)3 $\Rightarrow$ k=4 $\Rightarrow$ y=4x3 $\Rightarrow$ Hence y=4(3)3=108 is the value of y when x=3 A ball is dropped from the top of a building. The distance the ball falls is directly proportional to the square of the time it has been failling. If a ball falls 48 feet in 2 seconds, find how far it has fallen after 6 seconds. d=kt2 $\Rightarrow$ 48=k(2)2 $\Rightarrow$ 48=4k $\Rightarrow$ k=12 $\Rightarrow$ d=12t2 Hence d=12(6)2=432 is the distance the ball has fallen after 6 second.