Chapter 3 Introduction to Graphing and Equations of Lines Section 4 Slope-Intercept Form of a Line

Section 3.4 Objectives 1 Use the Slope-Intercept Form to Identify the Slope and y-Intercept of a Line 2 Graph a Line Whose Equation Is in Slope-Intercept Form 3 Graph a Line Whose Equation Is in the Form Ax + By = C 4 Find the Equation of a Line Given Its Slope and y-Intercept 5 Work with Linear Models in Slope-Intercept Form

The Slope-Intercept Form Slope-Intercept Form of an Equation of a Line An equation of a line with slope m and y-intercept b is Slope y-intercept

The Slope-Intercept Form Example: Find the slope and y-intercept of the line whose equation is x + 2y = 8. Subtract x from both sides. Divide both sides by 2. y-intercept Slope

The Slope-Intercept Form Example: Graph the line using the slope and y-intercept. x y 1 2 3 4 1 2 3 4 y-intercept Slope run = 2 rise = 3

The Slope-Intercept Form Example: Graph the line 4x + 3y = 12 using the slope and y-intercept. Put the equation in y = mx + b form. x y 1 2 3 4 1 2 3 4 4x + 3y = 12 3y = – 4x + 12 rise = – 4 run = 3 y-intercept Slope

Linear Models Example: According to a 1989 National Academy of Sciences Report, the recommended daily intake of calories for males between the ages of 7 and 15 can be calculated by the equation y = 125x + 1125, where x represents the boy’s age and y represents the recommended calorie intake. (a) What is the recommended caloric intake for a 14-year-old boy? (b) What is the age of a boy whose recommended caloric intake is 2375 calories? (c) Interpret the slope of y = 125x + 1125 in terms of rate of change. Continued.

Linear Models Example continued: (a) y = 125x + 1125 Substitute 14 for x. = 2875 The recommended intake for a 14-year-old boy is 2375 calories. (b) y = 125x + 1125 2375 = 125x + 1125 Substitute 2375 for y. 1250 = 125x 10 = x 2375 calories would be the recommended intake for a 10-year-old boy. (c) The recommended caloric intake increases by 125 calories per year.