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**Linear Equations in Two Variables**

Objective: Write a linear equation in two variables given different types of information.

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Example 1

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Example 1

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Example 1

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Example 1

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope Find the y-intercept

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope Find the y-intercept Write an equation

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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.

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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.

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope Use point-slope form

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Try This Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6) Find the slope Use point-slope form

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Example 2

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Example 2

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Example 2

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Try This Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1).

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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

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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 Write an equation

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**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.

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Parallel Lines

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Example 4

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Example 4

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Example 4

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Example 4

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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.

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Perpendicular Lines

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Example 5

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Example 5

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Example 5

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Example 5

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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?

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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).

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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).

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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.

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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!

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Writing Equations of Lines. Find the equation of a line that passes through (2, -1) and (-4, 5).

Writing Equations of Lines. Find the equation of a line that passes through (2, -1) and (-4, 5).

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