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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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 , 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 in terms of rate of
change.
Continued.

8. 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
2375 = 125x
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.