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Published byJoshua Weaver Modified over 4 years ago

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4 minutes Warm-Up 1) Find the slope of the line containing the points (-1,12) and (5,-6). 2) Identify the slope and y-intercept for the line y = -5x + 7. 3) Write the equation in slope-intercept form for the line that has a y-intercept of 0 and a slope of -1.

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**1.3.1 Linear Equations in Two Variables**

Objectives: Write a linear equation in two variables given sufficient information

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Example 1 Write an equation for the line containing the points (1,5) and (2,8).

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**Example 1 y = mx + b 5 = 3 (1) + b 5 = 3 + b -3 -3 2 = b y = 3x + 2**

Write an equation for the line containing the points (1,5) and (2,8). y = mx + b substitute 5 = 3 (1) + b simplify 5 = 3 + b -3 -3 2 = b y = 3x + 2

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**The Point-Slope Equation**

y – y1 = m(x – x1)

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Example 2 Write an equation for the line with slope 7 that contains the point (3,4). y – y1 = m(x – x1) y – 4 = 7(x – 3) y – 4 = 7x - 21 y = 7x - 17

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Example 3 Write an equation for the line containing (5,7) and (2,1). First, find the slope: y – y1 = m(x – x1) y – 7 = 2(x – 5) y – 7 = 2x - 10 y = 2x - 3

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Example 4 Write an equation for the line shown below. First, find any two points on the line. (-3,-3) and (1,-1) 4 2 -4 -2 2 4 y – y1 = m(x – x1) -2 -4 y + 3 = ½(x + 3) y + 3 = ½x + 1½ y = ½x – 1½

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Example 5 Marva left her house and drove at a constant speed to a conference in another state. She picked up Delia along the way. Two hours after picking up Delia, they were 140 miles from Marva’s house, and 5 hours after picking up Delia, they were 344 miles from Marva’s house. How far from her house was Marva when she picked up Delia?

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Homework p.26 #11-31 odds

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4 minutes Warm-Up Write an equation for the line given the indicated points. 1) (-6,-6) and (-3,1) Write an equation in point-slope form for the line that has the indicated slope, m, and contains the given point. 2) m = 4; (9,-3)

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**1.3.2 Linear Equations in Two Variables**

Objectives: Write an equation for a line that is parallel or perpendicular to a given line

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Activity Graph y = 2x + 1. On the same screen, graph y = 2x, y = 2x – 2.5, and y = 3x + 1. Which equations have graphs that appear to be parallel to that of y = 2x + 1? y = 2x, y = 2x – 2.5 What do these equations have in common? same slopes Write an equation in slope-intercept form for a line whose graph you think will be parallel to that of y = 2x Verify by graphing.

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**Activity Graph y = 2x + 1. On the same screen, graph**

Which equations have graphs that appear to be perpendicular to that of y = 2x + 1? What do these equations have in common? their slopes are negative reciprocals of each other

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Activity Write an equation in slope-intercept form whose graph you think will be perpendicular to that of y = 2x Verify by graphing.

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Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

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Perpendicular Lines Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8 The product of the slopes of perpendicular lines is -1.

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**Example 1 Determine whether these lines are parallel or perpendicular.**

y – 2 = 5x + 4 and -15x + 3y = 9 +15x x y = 5x + 6 3y = x y = 3 + 5x y = 5x + 3 The lines have the same slope. So they are parallel.

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Example 2 Write an equation in slope-intercept form for the line containing (-3,-5) and parallel to the line y = 2x + 1. m = 2 First, we need the slope of the line y = 2x + 1. Second, we need to find out the slope of the line that is parallel to y = 2x + 1. Lastly, we use the point-slope formula to find our equation. y + 5 = 2x + 6 y = 2x + 1

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Example 3 Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1. First, we need the slope of the line y = 2x + 1. m = 2 Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1. Lastly, we use the point-slope formula to find our equation.

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Homework p.26 #35-51 odds

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SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.

SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.

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