VIEWS: 3 PAGES: 40 POSTED ON: 1/7/2012
Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information. 6 12 18 3 5 1 6 m 5; b 7 y 1x 0 y x Example 1 Example 1 Example 1 Example 1 Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 2) Find the y-intercept y mx b 4 (2)( 2) b 8b Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 2) Find the y-intercept y mx b 4 (2)( 2) b 8b 3) Write an equation y mx b y 2 x 8 Point-Slope Form • You can use the point-slope form to write an equation of a line if you are given the slope and the coordinates of any point on the line or given two points. Point-Slope Form • You can use the point-slope form to write an equation of a line if you are given the slope and the coordinates of any point on the line or given two points. Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 2) Use point-slope form y y1 m( x x1 ) y 4 2( x 2) y 4 2 x 4 y 2 x 8 Try This • Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) 64 2 1) Find the slope 2 1 2 1 2) Use point-slope form y y1 m( x x1 ) y y1 m( x x1 ) y 4 2( x 2) y 6 2( x 1) y 4 2 x 4 y 6 2 x 2 y 2 x 8 y 2 x 8 Example 2 Example 2 Example 2 Try This • Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1). Try This • Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1). • Begin with point-slope form y y1 m( x x1 ) y (1) 3( x 2) Try This • Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1). • Begin with point-slope form y y1 m( x x1 ) y (1) 3( x 2) • Write an equation y 1 3x 6 y 3x 7 Parallel Lines • If two lines have the same slope, they are parallel. • If two lines are parallel, they have the same slope. • All vertical lines have an undefined slope and are parallel to one another. • All horizontal lines have a slope of 0 and are parallel to one another. Parallel Lines Example 4 Example 4 Example 4 y mx b 3 (2)(1) b 1 b y 2 x 1 Example 4 y mx b 3 (2)(1) b 1 b y 2 x 1 Perpendicular Lines • If a nonvertical line is perpendicular to another line, the slopes of the lines are negative reciprocals of one another. • All vertical lines are perpendicular to all horizontal lines. • All horizontal lines are perpendicular to all vertical lines. Perpendicular Lines Example 5 Example 5 Example 5 y mx b 3 ( 1 )(4) b 4 2b y 1 x2 4 Example 5 Example 3 • Tim leaves his house and drives at a constant speed to go camping. On his way to the campgrounds, he stops to buy gas. Three hours after buying gas, Tim has traveled 220 miles from home, and 5 hours after buying gas he has traveled 350 miles from home. How far from home was Tim when he bought gas? Example 3 • Write a linear equation to model Tim’s distance, y, in terms of time, x. Three hours after buying gas, Tim has traveled 220 miles, and 5 hours after buying gas, Tim has traveled 350 miles. The line contains the points (3, 220) and (5, 350). Example 3 • Write a linear equation to model Tim’s distance, y, in terms of time, x. Three hours after buying gas, Tim has traveled 220 miles, and 5 hours after buying gas, Tim has traveled 350 miles. The line contains the points (3, 220) and (5, 350). Example 3 • This equation models Tim’s distance from home with respect to time. Since x represents the number of hours he traveled after he bought gas, he bought gas when x = 0. Thus, he bought gas 25 miles from home. Homework • Pages 26-27 • 11-45 odd • Please check your answers as you go and do all of the problems. You need practice to master this skill!