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# Chapter 11.2 Slope of a Line

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#### Transcript of Chapter 11.2 Slope of a Line

Chapter 11.2 Slope of a Line Review Slope: A measure of steepness of a line on

a graph; the rise divided by the run.

Positive Slope: Negative Slope: Vertical change Horizontal change = rise run Examples of Slopes Positive Slope Negative Slope Zero slope Undefined slope If you know any two points

on a line, or two solutions of

a linear equation, you can find

the slope of the line without

graphing. The slope of the line

through the points (x1,y1)

and (x2,y2) are: x2-x1 Example 1 Finding slope, given two points BY: Alexis Noble and Tia Moses 8x4=32 -9<9 3x=6 9^2=81 60 7 (x,y) I <3 Prealgebra Find the slope of the line that passes through (2,5) and (8,1) Let (x1, y1) be (2,5) and (x2, Y2) be (8,1) y2-y1 = 1-5 x2-x1 = 8-2 Substitute 1 for y2, 5 for y1, 8 for x2, and 2 for x1. = -4 6 = 2 3 - The slope of the line that passes through (2,5) and (8,1) is - 2 3 Example 1 continued When choosing two points to evaluate the slope of a line, you can choose any two points on the line because the slope is constant.

Below are two graphs of the same line. -2 0 2 -2 x y (-2,-2) (-1,0) y2-y1 x2-x1 = 0 - (-2) -1 - (-2) = 2 1 = 2 0 -2 2 2 -2 x y (-2,-2) (0,-2) y2-y1 x2-x1 = 2 - (-2) 0 - (-2) = 4 2 = 2 1 = 2 The slope of the line is 2. Notice that although different points were chosen in each case, the slope formula still results in the same slope for the line. Example 2 0 -2 2 -2 2 y x Choose two points on the line: let's use (-1,2) and

(2,0).

Guess by looking at the graph: run = 2 3 - Use the slope formula.

Let (2,0) be (x1,y1) and (-1,2) be (x2,y2) y2 - y1 x2-x1 = 2 -0 -1 -2 = 2 -3 = 2 3 - Helpful Hint It doesn't matter

which point is chosen

as (x1,y1) and which

point is chosen as (x2,y2) Notice even if you switch (x1, y1) and (x2, y2), you get the same slope. Example 3 Recall that two parallel lines have the same slope. The slopes of two perpendicular lines are negative

reciprocals of each other. A. line 1: (1,9) and (-1,5) ; line 2: (-3, -5) and (4,9)

slope of line 1: y2 - y1 x2-x1 = 5 -9 -1 -1 = -4 -2 = 2 slope of line 2: y2- y1 x2-x1 = 9 - (-5) 4 - (-3) = 14 7 = 2 B. line 1: (-10, 0) and (20, 6) ; line 2:

(-1, 4) and (2, -11) slope of line 1: y2 - y1 x2-x1 = 6 -0 20 -(-10) = 6 30 = 1 5 slope of line 2: y2- y1 x2-x1 = -11 - 4 2 - (-1) = -15 3 = -5 Line 1 has a slope equal to 1/5 and line 2 has a slope equal to -5. 1/5 and -5 are negative reciprocals of each other, so they are perpendicular. Example 4 Graph the line passing through (1,1) with slope -1/3. The slope is - 1/3. So for every 1 unit down, you will move 3 units to the right, and for every 1 unit up, you will move 3 units to the left.

Plot the point (1,1). Then move 1 unit down and right 3 units and plot the point (4,0). Use a straitedge to connect the two points. 0 -2 -4 -2 -4 2 4 2 4 +3 units -1 unit You try it :) A. Find the slope of the line that passes through each pair of points. 1. (2,6) and (0,2)

2. (-1,2) and (5,5) B. Use the graph of the line to determine its slope. x y 2 -2 -2 2 0 C. Tell whether the lines passing through the given points are parallel or perpendicular. line 1: (2,3) and (4,7)

line 2: (5,2) and (9,0) The End!!! :)))) ThAnKs FoR LiStEnInG!!! y2-y1 rise

Full transcripta graph; the rise divided by the run.

Positive Slope: Negative Slope: Vertical change Horizontal change = rise run Examples of Slopes Positive Slope Negative Slope Zero slope Undefined slope If you know any two points

on a line, or two solutions of

a linear equation, you can find

the slope of the line without

graphing. The slope of the line

through the points (x1,y1)

and (x2,y2) are: x2-x1 Example 1 Finding slope, given two points BY: Alexis Noble and Tia Moses 8x4=32 -9<9 3x=6 9^2=81 60 7 (x,y) I <3 Prealgebra Find the slope of the line that passes through (2,5) and (8,1) Let (x1, y1) be (2,5) and (x2, Y2) be (8,1) y2-y1 = 1-5 x2-x1 = 8-2 Substitute 1 for y2, 5 for y1, 8 for x2, and 2 for x1. = -4 6 = 2 3 - The slope of the line that passes through (2,5) and (8,1) is - 2 3 Example 1 continued When choosing two points to evaluate the slope of a line, you can choose any two points on the line because the slope is constant.

Below are two graphs of the same line. -2 0 2 -2 x y (-2,-2) (-1,0) y2-y1 x2-x1 = 0 - (-2) -1 - (-2) = 2 1 = 2 0 -2 2 2 -2 x y (-2,-2) (0,-2) y2-y1 x2-x1 = 2 - (-2) 0 - (-2) = 4 2 = 2 1 = 2 The slope of the line is 2. Notice that although different points were chosen in each case, the slope formula still results in the same slope for the line. Example 2 0 -2 2 -2 2 y x Choose two points on the line: let's use (-1,2) and

(2,0).

Guess by looking at the graph: run = 2 3 - Use the slope formula.

Let (2,0) be (x1,y1) and (-1,2) be (x2,y2) y2 - y1 x2-x1 = 2 -0 -1 -2 = 2 -3 = 2 3 - Helpful Hint It doesn't matter

which point is chosen

as (x1,y1) and which

point is chosen as (x2,y2) Notice even if you switch (x1, y1) and (x2, y2), you get the same slope. Example 3 Recall that two parallel lines have the same slope. The slopes of two perpendicular lines are negative

reciprocals of each other. A. line 1: (1,9) and (-1,5) ; line 2: (-3, -5) and (4,9)

slope of line 1: y2 - y1 x2-x1 = 5 -9 -1 -1 = -4 -2 = 2 slope of line 2: y2- y1 x2-x1 = 9 - (-5) 4 - (-3) = 14 7 = 2 B. line 1: (-10, 0) and (20, 6) ; line 2:

(-1, 4) and (2, -11) slope of line 1: y2 - y1 x2-x1 = 6 -0 20 -(-10) = 6 30 = 1 5 slope of line 2: y2- y1 x2-x1 = -11 - 4 2 - (-1) = -15 3 = -5 Line 1 has a slope equal to 1/5 and line 2 has a slope equal to -5. 1/5 and -5 are negative reciprocals of each other, so they are perpendicular. Example 4 Graph the line passing through (1,1) with slope -1/3. The slope is - 1/3. So for every 1 unit down, you will move 3 units to the right, and for every 1 unit up, you will move 3 units to the left.

Plot the point (1,1). Then move 1 unit down and right 3 units and plot the point (4,0). Use a straitedge to connect the two points. 0 -2 -4 -2 -4 2 4 2 4 +3 units -1 unit You try it :) A. Find the slope of the line that passes through each pair of points. 1. (2,6) and (0,2)

2. (-1,2) and (5,5) B. Use the graph of the line to determine its slope. x y 2 -2 -2 2 0 C. Tell whether the lines passing through the given points are parallel or perpendicular. line 1: (2,3) and (4,7)

line 2: (5,2) and (9,0) The End!!! :)))) ThAnKs FoR LiStEnInG!!! y2-y1 rise