Eysasurbanoidn
Answered

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V.
Give the slope of a line given two points.
17. (-2,4) and (1,6)
18. (-3,-1) and (5,-5)​

Sagot :

KAntoineDoixidn

✏️SLOPES

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[tex] \underline{\mathbb{DIRECTIONS}:} [/tex]

Give the slope of a line given two points.

  • 17. (-2, 4) and (1, 6)
  • 18. (-3, -1) and (5, -5)

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[tex] \underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad\large 17) \LARGE\tt\: \green{\frac{\,4\,}{3}} [/tex]

[tex] \qquad\large 18) \LARGE \tt\: \green{\text-\frac{\,1\,}{2}} [/tex]

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[tex] \underline{\mathbb{SOLUTION}:} [/tex] Use the slope formula to find the slope of the given two points.

[tex] \begin{align} & \bold{Formula:} \\ & \boxed{Slope(m) = \frac{y_2-y_1}{x_2-x_1}} \end{align} [/tex]

#17:

  • [tex] m = \frac{6-2}{1-(\text-2)} \\ [/tex]

  • [tex] m = \frac{6-2}{1+2} \\ [/tex]

  • [tex] m = \frac{\,4\,}{3} \\ [/tex]

[tex] \therefore [/tex] The slope of the given two points is 4/3.

#18:

  • [tex] m = \frac{\text-5-(\text-1)}{5-(\text-3)} \\ [/tex]

  • [tex] m = \frac{\text-5 + 1}{5 + 3} \\ [/tex]

  • [tex] m = \frac{\,\text-4\,}{8} \\ [/tex]

  • [tex] m = \text{ -- }\frac{\,1\,}{2} \\ [/tex]

[tex] \therefore [/tex] The slope of the given two points is -1/2.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]

(ノ^_^)ノ

MrIvanidn

[tex] \red{•••••••••••••••••••••••••••••••••••••••••••••}[/tex]

QUSTION:

Give the slope of a line given two points.

(#17.)

FORMULA:

∵The slope of a line passing through the two points.

  • [tex]P = (^{x}2 ,^{y} 2) \\ [/tex]
  • [tex]Q = ( ^{x} 2.^{y} 2) \\ [/tex]
  • [tex]M = \frac{^{y} 2 - ^{y} 1}{^{x}2 - ^{x} 1 } \\ [/tex]

∵Plug the given values into the formula for slope.

  • [tex]m = \frac{(6) - (4)}{(1) - (2)} = \frac{2}{ - 1} = - 2 \\ [/tex]

∵Now, the y-intercept is

  • [tex] \boxed{ b = ^{y}1 - m \: \times ^{x}1 }[/tex]

  • [tex] \boxed{b = ^{y} 2 - m \: \times ^{x} 2}[/tex]

∵The result is the same.

  • [tex] \boxed{b = 4 - ( - 2) \times (2) = 8 .}[/tex]

∵Finally, the equation of the line can be written in the form.

  • y=mx+b

  • [tex]y=−2x+8.[/tex]

»The slope of the line is

  • [tex] \boxed{ \frac{4}{3} }[/tex]

(#18.)

  • [tex] \boxed{(-3,-1) and (5,-5)}[/tex]

  • [tex]m = \frac{( - 5) - ( - 1)}{(5) - ( - 3)} = \frac{ - 4}{8} = - \frac{ 1}{2} \\ [/tex]

  • [tex]b = - 1 - ( - \frac{1 }{2} ) \times ( - 3) = - \frac{5}{2} \\ [/tex]

  • [tex]y = - \frac{1}{2} x - \frac{5}{2} . \\ [/tex]

Result:

  • [tex] \boxed{m = - \frac{1}{2} } \\ [/tex]

[tex] \red{••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnLearning

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