1.1 Lines in a Plane Finding the slope of a line

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Presentation transcript:

1.1 Lines in a Plane Finding the slope of a line Using Point-Slope form of the equation of a line Using Slope-Intercept form of the equation of a line Using General (Standard) form of the equation of a line Finding the equations of parallel and perpendicular lines

The slope m of a line through the points

Example 1 Find the slope of the line passing through each pair of points (-2,0) and (3,1)

Find the slope of the line containing (-1,2) and (2,2)

Find the slope of the line containing (0,4) and (1,-1)

Student Example Find the slope of a line containing the points (-4,6) and (5,-2)

Lines may take 4 different forms: Positive Slope Negative Slope Slope of Zero Undefined Slope

The Point-Slope Form of a Line The line passing through the point and has a slope of m can be written

Example 2 Find an equation of a line that passes through the point (1,-2) and has a slope of 3.

Slope-Intercept Form y=mx+b where m is the slope and (0,b) is the y-intercept Give the equation of a line passing through the point (1,-2) and has a slope of 3.

Student Example Find an equation of a line that passes through the point (2,-4) and has a slope of –2. Give the equation in point-slope form Give the equation in slope-intercept form

Example 3 During 2000, Nike’s net sales were $9 billion, and in 2001 net sales were $9.5 billion. Write a linear equation giving the net sales y in terms of the year x. Then use the equation to predict the net sales for 2002.

Example 4 Determine the slope and the y-intercept of each linear equation. a. x+y=2 b. y=2

Example 5 The graphs of y=-x-1 and y=-10x-1 are shown on p. 8. What is different about the graphing calculator that would make both graphs appear the same?

Example 6 Find the slope-intercept form of the equation of the line that passes through the point (2,-1) and is parallel to the line 2x-3y=5. *Hint – Parallel lines have the same slope

Student Example Find the slope-intercept form of the equation of the line that passes through the point (-2,4) and is parallel to the line x-2y=5.

Example 7 Find the slope-intercept form of a line that passes through the point (2,-1) and is perpendicular to the line 2x-3y=5 *Hint – Perpendicular lines have opposite reciprocal slope

Student Example Find the slope-intercept form of the equation of the line that passes through the point (-2,4) and is perpendicular to the line x-2y=5.

Example 8 Graph the lines y=x+1 and y=-x+3 on your graphing calculator. If these lines are suppose to be perpendicular, why don’t they appear as such on your calculator screen?

p. 11-12, 1st problem in each section p. 13-14 #65, 69, 71, 75-79