6.1 Slope of a Line Slope of a Line Segment The slope of a line segment is a measure of the steepness of the line segment. It is the ratio of rise (the change in vertical height between the endpoints) over run (the change in horizontal length between the endpoints. Slope = ௦ ௨ ୲୦ ୰୧ୱ ୧ୱ ୮୭ୱ୧୲୧୴ ୧ ୵ ୡ୭୳୬୲ ୳୮,ୟ୬ ୬ୟ୲୧୴ ୧ ୵ ୡ୭୳୬୲ ୭୵୬ ୲୦ ୰୳୬ ୧ୱ ୮୭ୱ୧୲୧୴ ୧ ୵ ୡ୭୳୬୲ ୰୧୦୲,ୟ୬ ୬ୟ୲୧୴ ୧ ୵ ୡ୭୳୬୲ ୪୲ Determine the Slope of a Line Segment Example 1. Determine the slope of each line segment. Line Segment Rise Run Slope AB CD EF Draw a Line Segment with a Given Slope Example 2. Draw a line segment with each given slope. (can put initial point anywhere) a) ହ (AB) b) െ ଷ (CD) Try. a) ସ ଽ (EF) b) െ ଷ (GH)
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Slope of a Line Segment rise run - Mr. Sardinhamrsardinha.weebly.com/uploads/1/2/3/8/12387189/6.1_notes...6.1 Slope of a Line Slope of a Line Segment The slope of a line segment is
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6.1 Slope of a Line Slope of a Line Segment The slope of a line segment is a measure of the steepness of the line segment. It is the ratio of rise (the change in vertical height between the endpoints) over run (the change in horizontal length between the endpoints. Slope = ,
,
Determine the Slope of a Line Segment Example 1. Determine the slope of each line segment.
Line Segment
Rise Run Slope
AB
CD
EF
Draw a Line Segment with a Given Slope Example 2. Draw a line segment with each given slope. (can put initial point anywhere) a) (AB) b) (CD)
Try. a) (EF) b) (GH)
Investigate the Slope of Line Segments on a Line Example 3. Complete the chart. Write the slopes in simplest form.
Line Segment
Rise Run Slope
AB
AC
AD
BC
Slope of a Line The slope of all line segments on the same line are equal; therefore, the slope of a line can be found by calculating rise over run from any segment on the line. Determine Slope Given Two Points on a Line Example 4. Determine the slope of the line passes through:
a) C(−5, −3) and D(2,1) b) E(4, −5) and F(8,6)
Slope of a Line Calculated Algebraically The slope, m, of a line passing through A(x1,y1) and B(x1,y1) can be determined by m =
Investigate the Directions and Slopes of Line Segments Example 5. Compare the slopes of the following line segments.
a) Calculate the slope of each line segment. b) Complete the following statements. Positive or Negative Slope
Rises from left to right
Falls from left to right
Investigate the Slopes of Horizontal and Vertical Line Segments Example 6. Consider the line segment in Grid 1 and Grid 2 below.
a) Determine the slopes of all the line segments in Grid 1.
b) Determine the slopes of all the line segments in Grid 2.
Slopes of Horizontal and Vertical Lines Horizontal line segments have a slope of zero. Vertical line segments have an undefined slope.
Interpret the Slope of a Line Example 7. Yvonne recorded the distances she had travelled at certain times since she began her cycling trip along the Trans Canada Trail in Manitoba, from North Winnipeg to Grand Beach. She plotted these data on a grid.
a) What is the slope of the line through these points? b) What does the slope represent?
c) How can the answer to part b be used to determine:
i) How far Yvonne travelled in 1 hours ? ii) How much time it took Yvonne to travel 55 km?
x‐intercept x‐intercept is the x‐coordinate of a point where a graph intersects the x ‐axis. y‐intercept y‐intercept is the y‐coordinate of a point where a graph intersects the y ‐axis.