3 Chapter Chapter 2 Graphing

Section 3.5 Equations of Lines

Using the Slope-Intercept Form to Graph an Equation Objective 1 Using the Slope-Intercept Form to Graph an Equation

Slope-Intercept Form Slope-Intercept Form of a line When a linear equation in two variables is written in slope-intercept form, y = mx + b then m is the slope of the line and (0, b) is the y-intercept of the line. slope (0, b), y-intercept

Example Use the slope-intercept form to graph the equation. The slope is 3/5. The y-intercept is –2. Begin by graphing (0, –2), move up 3 units and right 5 units.

Using the Slope-Intercept Form to Write an Equation Objective 2 Using the Slope-Intercept Form to Write an Equation

Example Find an equation of the line with y-intercept (0, –2) and slope 3/5.

Writing an Equation Given Slope and a Point Objective 3 Writing an Equation Given Slope and a Point

Point-Slope Form The point-slope form of the equation of a line is where m is the slope of the line and (x1, y1) is a point on the line.

Example y + 12 = –2x – 22 Use the distributive property. Find an equation of the line with slope –2 that passes through (–11, –12). Write the equation in slope-intercept form, y = mx + b, and in standard form, Ax + By = C. We substitute the slope and point into the point-slope form of an equation. y – (–12) = – 2(x – (– 11)) Let m = –2 and (x1, y1) = (–11, –12). y + 12 = –2x – 22 Use the distributive property. y = –2x – 34 Slope-intercept form. 2x + y = –34 Add 2x to both sides and we have standard form.

Writing an Equation Given Two Points Objective 4 Writing an Equation Given Two Points

Example Find an equation of the line through (–4, 0) and (6, –1). Write the equation in standard form. First, find the slope. Continued

Example (cont) Now substitute the slope and one of the points into the point-slope form of an equation. 10y = –1(x + 4) Clear fractions by multiplying both sides by 10. 10y = –x – 4 Use the distributive property. x + 10y = –4 Add x to both sides.

Finding Equations of Vertical and Horizontal Lines Objective 5 Finding Equations of Vertical and Horizontal Lines

Example Find an equation of the vertical line through (–7, –2). The equation of a vertical line can be written in the form x = c, so an equation for a vertical line passing through (–7, –2) is x = –7.

Example Find an equation of the line parallel to the line y = –3 and passing through (10, 4). Since the graph of y = –3 is a horizontal line, any line parallel to it is also horizontal. The equation of a horizontal line can be written in the form y = c. An equation for the horizontal line passing through (10, 4) is y = 4.

Using the Point-Slope Form to Solve Problems Objective 6 Using the Point-Slope Form to Solve Problems

Example In 1997, Window World , Inc. had 50 employees. In 2012, the company had 85 employees. Let x represent the number of years after 1997 and let y represent the number of employees. a.) Assume that the relationship between years and number of employees is linear, write an equation describing this relationship. b.) Use the equation to predict the number of employees in 2007. Continued

Example (cont) Continued a. The year 1997 is represented by x = 0. 2012 is 15 year after 1997, so 2012 is represented by x = 15. The two points (0, 50) and (15, 85) will be used to find the equation. Substitute the values for m, x1, and y1. Distribute. Add 50 to both sides. Continued

Example (cont) Use the equation to predict the number of employees in 2007. In 2007, x = 10.