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allochka39001 [22]
2 years ago
7

Line Equation from Two Points

Mathematics
1 answer:
Verdich [7]2 years ago
7 0

Hi!

We can use <u>point-slope form </u>to solve this.

y-y_{1} =m(x -x_{1})

y_{1}<em> and </em>x_{1}<em> will be from one of the points.</em>

<u>First, we have to find </u>m<u>, the slope. We can use the slope equation to get this.</u>

\frac{y_{1} -y_{2} }{x_{1} -x_{2} }

<em>Plug in your points:</em>

\frac{4-0}{8-(-8)} =\frac{4-0}{8+8} =\frac{4}{16} =\frac{1}{4}

Your slope is \frac{1}{4}

<u><em>Now plug points and slope into point-slope equation. We will use (8, 4).</em></u>

y-4=\frac{1}{4} (x-8)

Now, if you want to get it into y = mx + b form, you have to solve for y:

y-4=\frac{1}{4} (x-8)

y-4=\frac{1}{4} x-2

y=\frac{1}{4} +2

Your equation is y=\frac{1}{4} +2

<u><em>For more information on how to get the equation of a line when given two points, see here:</em></u>

brainly.com/question/986503

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Some members of the cooking club are making cakes which they will sell at a street fair for $10 apiece. It costs $10 for a booth
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The cooking club sales covers the expenditure when 2 piece of cakes are sold.

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We need to find the number of pieces of cake sold when the sales cover the expenditures.

Solution:

Let the number of pieces be 'x'

So We can say that the point at which the sales cover the expenditures can be calculated as Selling price of each piece of cake multiplied by number of pieces will be equal to Cost for booth at fair plus Ingredients for each piece of cake multiplied number of piece of cakes.

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How can I factor 5x^2 + 26x - 24 = 0 using the completing the square method.
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<h2><u>QUADRATIC EQUATION</u></h2>

<h2>\mathbb{ANSWER:}</h2>
  • \bold{x = 0.8 \: } \:  \sf \:  {\color{grey}or} \:  \:  \:  \bold{ x=  \frac{4}{5} } \\

  • \bold{x =  - 6}

— — — — — — — — — —

<h3>Step-by-step explanation:</h3>

<u>How can </u><u>we</u><u> factor 5x^2 + 26x - 24 = 0 using the completing the square </u><u>method?</u>

Let's solve your equation step-by-step.

\bold{Given \:  Equation: \color{brown} 5x²+26x-24=0}

First, add 24 to both sides.

  • \bold{5x²+26x-24 - \purple{ 24} = 0 +  \purple{24}}

  • \bold{ \implies \: 5x²+26x = 24 }

Since the coefficient of 5x² is 5, divide both sides by 5.

  • \bold{ \frac{5 {x}^{2} + 26x }{5} =  \frac{24}{5}  } \\

  • \bold{ \implies \:  {x}^{2} +  \frac{26}{5} x =  \frac{24}{5}  } \\

The coefficient of 26/5x is 26/5. So, let b=26/5.

Then we need to add (b/2)²=169/25 to both sides to complete the square.

Add 169/25 to both sides.

  • \bold{ {x}^{2} +  \frac{26}{5} x +  \frac{  \purple{169}}{ \purple{25}}=  \frac{24}{5}    +  \frac{ \purple{169}}{ \purple{25}} } \\

  • \bold{ \implies \:\bold{ {x}^{2} +  \frac{26}{5} x +  \frac{  169}{ {25}}=  \frac{289}{25}  } } \\

Factor the left side.

  • \bold{(x +  \frac{13}{5} ) {}^{2} =  \frac{289}{25}  } \\

Take square root.

  • \bold{x +  \frac{13}{5} = ±  \:  \sqrt{ \frac{289}{25}  }} \\

Then, add (-13)/5 to both sides.

  • \bold{x +  \frac{13}{5} +  \frac{\purple{ - 13} }{\purple{ 5}} = \frac{{ - 13} }{{ 5}} ± \:      \sqrt{ \frac{289}{25}}} \\

  • \bold{  \: x =  \frac{ - 13}{5} ± \sqrt{ \frac{289}{25} } } \\

  • \implies \: \underline{ \boxed{ \bold{   \frac{4}{5}  } \sf  \:  \: or \:  \:  \bold{ x =  - 6}}} \\

_______________❖_______________

3 0
3 years ago
Read 2 more answers
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