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The figures below depict pairs of parallel lines. Write down the formula for the line whose graph goes through:

The origin in figure a
Point (0, 3) in figure b

The figures below depict pairs of parallel lines. Write down the formula for the line-example-1

1 Answer

3 votes

Answer:

a) The formula for the figure A is
y = -x, b) The formula for the figure B is
y = -x +3-

Explanation:

From Analytical Geometry, we know that two lines are parallel to each other when they share the same slope. We get the slope of figure B by means of the slope formula:


m = (y_(2)-y_(1))/(x_(2)-x_(1))

Where:


x_(1),
x_(2) - Initial and final x-coordinates, dimensionless.


y_(1),
y_(2) - Initial and final y-coordinates, dimensionless.


m - Slope, dimensionless.

If we know that
(x_(1), y_(1)) = (0, 3) and
(x_(2), y_(2)) = (3, 0), the slope of both lines is:


m = (0-3)/(3-0)


m = -1

Any line is described by the following formula:


y = m\cdot x + b

Where:


x - Independent variable, dimensionless.


y - Dependent variable, dimensionless.


m - Slope, dimensionless.


b - y-Intercept, dimensionless.

The y-Intercept is cleared within the formula:


b = y-m\cdot x

Now we get the formula for each line depicted on figure:

a) The origin in figure a:
(x, y) = (0, 0),
m = -1


b = 0 - (-1) \cdot (0)


b = 0

The formula for the figure A is
y = -x.

b) Point (0, 3) in figure b:
(x, y) = (0, 3),
m = -1


b = 3 - (-1)\cdot (0)


b = 3

The formula for the figure B is
y = -x +3-

User Monkey Boson
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