Mathematics: Awalking path across a park is represented by the equation y = –2x - 7. a new path will be built perpendicular to this path. the paths will intersect at the point (-2, –3). identify the equation that represents the new path.

Awalking path across a park is represented by the

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13.03.2022

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

Step-by-step explanation:

Point slope intercept form:

The equation of lien is given by:

y-y_1 =m(x-x_1) .....[1]

where, m is the slope and (x_1, y_1) is the point on the line.

As per the statement:

A walking path across a park is represented by the equation

y = -2x -7.

On comparing with y =mx+b we have;

m_1 = -2

It is given that: A new path will be built perpendicular to this path.

By definition of perpendicular:

$m_1 \times m_2 = -1$

then;

$-2 \times m_2 = -1$

⇒ $m_2 = \frac{1}{2}$ , where m_2 is the slope of the new path.

Since, the new path will intersect at the point (-2, –3).

Substitute the given values in [1] we have;

$y-(-3)=\frac{1}{2}(x-(-2))$

⇒ $y+3 = \frac{1}{2}(x+2)$

⇒ $y+3 = \frac{1}{2}x+1$

Subtract 3 from both sides we have;

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

Therefore, the equation that represents the new path. is, $y= \frac{1}{2}x-2$

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