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allochka39001 [22]
2 years ago
7

Are the two lines x+2y=7 and 2x+4y=21 parallel or perpendicular?

Mathematics
1 answer:
Nezavi [6.7K]2 years ago
8 0

Answer:

They are parallel

Step-by-step explanation:

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Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.
Alexxandr [17]

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

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Then the constant C can be found using either point.

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The equation of the line is ...

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_____

<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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