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Unit 6- Linear Functions Vocabulary Lesson 21 – Slope The steepness of the line is called the slope. The slope shows the rate at which tow quantities are changing. Specifically, it is the ratio of the vertical change to the horizontal change, or rise . run Symbols and Formulas Slope: rise y run x y y2 1 x1 x2 m Slope-Intercept Form: y mx b m is the slope b is the y-intercept Point-Slope Form: y y1 m( x x1 ) m is the slope (x1, y1) is point on line Direct Proportion: y mx or y m x m is constant of proportionality. Similar triangles have the same shape, but not necessarily the same size. The ratios of the lengths of their corresponding sides are equal Lesson 22 – Slopes and y-intercepts The point at which the graph crosses the y-axis is called the yintercept. Any point (0,b) that is a solution of the equation is the y-intercept. The equation y = 2x+5 is written in a special form called the slope-intercept form. You can use the point-slope form to write the equation in slopeintercept form. Star Web Sites: School Site www.studyisland.com Ask Dr. Math http://mathforum.org/students/ Find instructions on math topics http://www.aaamath.com/ Math questions answered here http://www.mathnerds.com/mathne rds/index.asp Lesson 23 – Proportional Relationships A proportion shows that two ratios are equal in value. A unit rate is a rate that, when expressed as a fraction, has a 1 in the denominator. If a unit rate involves money, it is called a unit price. Lesson 24 – Direct Proportions Cool videos that explain math concepts! http://www.brainpop.com/math/ A direct proportion is a special kind of linear equation. In a direct proportion, the ratio of two variables, such as y an x, is a constant, m. We can say that y is directly proportional to x. Math help with games http://www.coolmath.com/home.ht m Math help by subject http://www.math.com/ A mathematical digital library http://www.mathdl.org/mathDL/ Lesson 25 – Work with Linear Functions A linear function is a special kind of function whose graph is a straight line (y=mx+b). A nonlinear function is any function that is not linear. Dependent variable is often called the y-value and the x-value is often called the independent variable. The initial value is the value of y when x equals 0. In a graph, the rate of change is the same as the slope. Lesson 26 – Compare Relationships in Different Ways none