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yawa3891 [41]
2 years ago
10

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Mathematics
1 answer:
Alexxandr [17]2 years ago
5 0

9514 1404 393

Answer:

  5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

  A = Δy = y2 -y1 = 2 -(-3) = 5

  B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

  5x -y = 5(-7) -2 = -37

The equation of the line is ...

  5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

  \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

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<h3>What are equations?</h3>
  • A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
  • a formula that expresses the connection between two expressions on each side of a sign.
  • Typically, it has a single variable and an equal sign.
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So, the equation of depreciation: y = A(1 - r)∧t

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Know more about equations here:

brainly.com/question/28937794

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