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Sagot :
Slope From Two Points
- (7,3) and (10,12)
[tex]M=\frac{rise}{run}=\frac{ᐃy}{ᐃx}[/tex]
[tex]M=\frac{y2 - y1}{x2-x1}[/tex]
[tex]M=\frac{12-3}{10-7}[/tex]
[tex]M=\frac{9}{3}[/tex]
[tex]\large\color{blue}\boxed{M=3}[/tex]
- (-3,7) and (1,5)
[tex]M=\frac{rise}{run}=\frac{ᐃy}{ᐃx}[/tex]
[tex]M=\frac{y2 - y1}{x2-x1}[/tex]
[tex]M=\frac{5-7}{1-(-3)}[/tex]
[tex]M=\frac{-2}{4}[/tex]
[tex]\large\color{blue}\boxed{M=\frac{-2}{4}}[/tex]
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[tex] \color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\underline{\mathbb{DIRECTION}:}[/tex]
- Find the slope given the pairs of points and give it's trend.
[tex]\qquad \qquad \sf \rm \: 1) \: (7,3) \: and \: (10 , 12) \\ \qquad \qquad\sf \rm 2) \: (-3,7) \: and \: (1,5)[/tex]
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\underline{\mathbb{SOLUTION}:}[/tex]
» When using two points , we can solve the slope using the rate of change in y and the change in x.
[tex]\sf \boxed{\qquad \sf \small \: Slope (m) = \frac{change \: in \: y}{change \: in \: x } = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex] \sf 1.) \: Given : P_1(7,3) \: ; \: P_2 (10,12) \\ \sf \:\qquad\qquad \small \: Slope (m) = \frac{change \: in \: y}{change \: in \: x } = \frac{y_2 - y_1}{x_2 - x_1} \\ \sf \small \: m = \frac{12 - 3}{10 - 7} \\ \sf \small \: m = \frac{9}{3} \\ \sf \boxed { \red { \sf \: m=3}}[/tex]
[tex]\therefore[/tex]Therefore, the slope [tex]\bold \red{(m)}[/tex] is [tex]\bold \red{3}[/tex].
[tex]\therefore[/tex] Trend : Increasing.
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex] \sf Given : P_1( - 3,7) \: ; \: P_2 (1,5) \\ \sf \:\qquad\qquad \small \: Slope (m) = \frac{change \: in \: y}{change \: in \: x } = \frac{y_2 - y_1}{x_2 - x_1} \\ \sf \small \: m = \frac{5 - 7}{1 - ( - 3)} \\ \sf \small \: m = \frac{ - 2}{ 4} \\ \sf \boxed { \red { \sf \: m= \frac{ -2 }{4} }}[/tex]
[tex]\therefore[/tex]Therefore, the slope [tex]\bold \red{(m)}[/tex] is [tex]\bold \red { \frac{ - 2}{4} }[/tex].
[tex]\therefore[/tex] Trend : decreasing.
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The slope tells us the trend of the linear equations.
- » If the slope is positive [tex]\bold \red{(+)}[/tex] , the line is increasing from left to right.
- » If the slope is negative [tex]\bold \red{(-)}[/tex] , the line is decreasing from left to right.
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
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