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Warm-Up 1) Find the slope of the line containing the points (-1,12) and (5,-6). 4 minutes 2) Identify the slope and y-intercept for the line y = -5x +

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Presentation on theme: "Warm-Up 1) Find the slope of the line containing the points (-1,12) and (5,-6). 4 minutes 2) Identify the slope and y-intercept for the line y = -5x +"— Presentation transcript:

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

2 1.3.1 Linear Equations in Two Variables Linear Equations in Two Variables Objectives: Write a linear equation in two variables given sufficient information

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

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

5 The Point-Slope Equation y – y 1 = m(x – x 1 )

6 Example 2 Write an equation for the line with slope 7 that contains the point (3,4). y – y 1 = m(x – x 1 ) y – 4 = 7(x – 3) y – 4 = 7x y = 7x - 17

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

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

9 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 Marvas house, and 5 hours after picking up Delia, they were 344 miles from Marvas house. How far from her house was Marva when she picked up Delia?

10 Homework p.26 #11-31 odds

11 Warm-Up Write an equation for the line given the indicated points. 4 minutes 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)

12 1.3.2 Linear Equations in Two Variables Linear Equations in Two Variables Objectives: Write an equation for a line that is parallel or perpendicular to a given line

13 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 + 1. Verify by graphing.

14 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

15 Activity Write an equation in slope-intercept form whose graph you think will be perpendicular to that of y = 2x + 1. Verify by graphing.

16 Parallel Lines Parallel lines are lines in the same plane that never intersect Parallel lines have the same slope.

17 Perpendicular Lines Perpendicular lines are lines that intersect to form a 90 0 angle The product of the slopes of perpendicular lines is -1.

18 Example 1 Determine whether these lines are parallel or perpendicular. y – 2 = 5x + 4and -15x + 3y = 9 +2 y = 5x x 3y = x 3 y = 3 + 5x y = 5x + 3 The lines have the same slope. So they are parallel.

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

20 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.

21 Homework p.26 #35-51 odds


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