Question

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

Answer 1

Answer:

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

Step-by-step 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:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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:

$m = \frac{0-3}{3-0}$

$m = -1$

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 $y = -x +3$-