SLOPE OF A LINE Learning Area: Curriculum Year: Proponent/Writer: School and Address: Least Learned Skill:
I.
Mathematics I First Year Jayson O. Daguro O¶Donnell High School Annex Sta. Juliana, Capas, Tarlac Finding the slope of a line passing through two points.
GUIDE CARD
Mountain climbers climbers are eager to reach reach the peak of the high ighest mountain in the wor ld. ld. Americ mericans, Chinese, Chinese, Ja panese, panese, Engl nglish ish, and and oth ot her foreigners have tried tried climbing climbing into it. it. Some has been succ successfu essfull but many of them fail failed. Even Fili pinos pinos tried tried to conquer the wor ld ld by climbing climbing the most dangerous part of the high ighest mountain in the wor ld, ld, the Mt. Everest. Dreamers like R omeo omeo Gar duce and and some oth ot her Fili pinos pinos onc once ex perien periencce the thrill rill of ful fulfill filling ing the dream, reach reaching ing the high ighest peak of the wor ld. ld. Hen Hencce, climbers climbers are wond ondering how stee p they go if t if they pass the north north, the south south, the east or t or the west direc irection of t of the mountain. mountain.
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In this sec section, let us ex plore plore and and find find out whi which direc irection is more convenient to satisfy the eagerness of conquering the wor ld ld by reach reaching ing the high ighest peak in the wor ld, ld, the Mt. Everest.
II.
Activity Card
Let us begin explori ng ng and find the slope of a line, but before that let·s have a review on the definition of a line and a oin oint. t.
Definition of Terms:
Geometric eometrically, lly, every line is a set of points containing at least two different points. oints. Moreover, any two different points bel belong to one and and onl only one line. ine. Algebrai Algebraiccally, lly, the line re presente presented d by the equation:
Ax + By + C = 0 Where Where A, B and and C are real real numbers, and and A and B are not equal equal to zero. ero.
A point point is re presente presented d by a dot and and shows position on a plane plane.. pness or incl inclination ination of a of a line is calle lled slope. The stee pness
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Activity Activity 1. To find find the stee pness pness of a hill you may determine the vertic vertical rise for every 100 ft of horiz orizontal ontal
run. run. For exam ple, ple, if a hill rises 20 ft for every 100 ft of horiz orizontal ontal distan d istancce, its stee pness pness is the ratio 20/100 or 20%.
Figure 1.
rise = 20 ft
20%
run = 100 ft
Simil imilar ly, to desc escribe the incl inclination ination or slo pe pe of a line, you choose choose two points on it to com pute pute the quotient. quotient. slo pe pe = rise = vertic vertical change change run horiz orizontal ontal change change Because the vertic vertical change ch ange is moving from one point to anoth another is the differenc ifference of the or dinates and and the horiz orizontal ontal change change is the corres pon pond ding change change differenc ifference of t of the absc abscissa. issa. Slo Slo pe pe = differen differencce of or of or dinates differenc ifference of abs of absccissa find the slo pe pe of a of a line algebraic gebraically, lly, consid onsider t er the equation: To find m = y2 ± y ± y1 x2 ± x ± x1 where: where: m ± is ± is the slo pe pe of t of the line y2 ± y ± y1 ± change change in y (differen (differencce of or of or dinates) x2 ± x ± x1 ± change change in x (differen (differencce of abs of absccissa)
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Exam ple ple 1. Find ind the slo pe pe of a of a line passing through rough (3, 2) and and (4, 5).
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Solution: Let: x1 = 3; x2 = 4; y1 = 2; y2 = 5 Substitute each each val value on the equation: m = y2 ± y ± y1 = 5 ± 2 = 3 x2 ± x ± x1 4 ± 3 Therefore, the slo pe pe of t of the line passing through rough (3, 2) and and (4, 5) is 3.
4, 5
4
3
2
3, 2
1
0 0
1
2
3
4
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Exam ple ple 2. Find ind the slo pe pe of a of a line through rough (1, (1, 1) and and (5, (5, 3) Solution: Let: x1 = 1; x2 = 5; y1 = 1; y2 = 3
3.5 3 5, 3
Substitute each each val value on the equation: m = y2 ± y ± y1 = 3 ± 1 = 2 x2 ± x ± x1 5 ± 1 4 pe of t of the line passing through rough Therefore, the slo pe (1, (1, 1) and and (5, (5, 3) is ½.
2.5 2 1.5 1 1, 1 0.5 0 0
1
2
3
4
5
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Activity 2. Anoth nother way of che checking the slo pe pe is counting the number of units on the rise and and the number of number of units units on the run. run.
4.5
Exam ple ple 3.
-4, 4 4 3.5
m = rise = 2 = _ 2 3 run -3
3 2.5
Counting 3 units from the point going to the left, the run is -3 and and counting counting 2 units going u p, p, the rise is +2; therefore the slo pe pe is -2/3.
-1, 2 2 1.5 1 0.5 0
-5
-4
-3
-2
-1
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III. Assessment Card A. Find ind the slo pe pe of t of the line passing through rough given points and and dra draw w the line. ine. 1. (3, 1); (5, (5,4) (0, 2) 2. (-2, 3); (0, 3. (3, -1) -1); (3, 4) 4. (4, 2); (-3, 2)
5. (2, 4); (-1, (-1, -1) -1)
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IV. Enrichment Enrichment Card Car d Solve the following:
1. Find ind the slo pe pe of a of a line passing through rough (0, (0, 5) and and (-6, 8).
2. A ladder dder is leaning 6 meters away from a build building ing reach reacheed 12 meters high igh from the
ground. ground. Fin Find d the incl inclination ination of t of the ladder dder .
3. Find ind the slo pe pe of a of a line containing (2, 10) 10) and and (-2, 8).
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V.
Reference Card Slope is the stee pness pness or t or the incl inclination ination of a of a line. ine. Math Mathematic ematically, lly, it is the ratio of verti of verticca l change change or ch or change ange in y calle lled rise and and hori horizzontal ontal change change or change change in x know known as the run.
Slo Slo pe pe =
The
rise run
=
vertic vertical change change = horiz orizontal ontal change change
change change in y change change in x
slo pe pe of a of a line passing through rough two points is determined etermined by the equation: m = y2 ± y1 x2 ± x1
where: where: m ± is ± is the slo pe pe of t of the line y2 ± y1 ± change change in y (differen (differencce of or of or dinates) change in x (differen (differencce of abs of absccissa) x2 ± x1 ± change
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