Question

A new four way intersection is being constructed in New York Hyde park through point P(-3,-15) an equation of the line representing one road is y = -3/4x + 7 create an equation of the line representing the new road that will run perpendicular to the first road

Answer 1

Given:

A new four way intersection is being constructed in New York Hyde park through point P(-3,-15).

Equation of line of one road :
`y=-(3)/(4)x+7`.

New road that will run perpendicular to the first road

To find:

The equation of line for the new road.

Solution:

The slope intercept form of a line is

`y=mx+b`

where, m is slope and b is y-intercept.

We have,

`y=-(3)/(4)x+7`

Slope of this line is
`-(3)/(4)` and y-intercept is 7.

Product of slopes of two perpendicular line is -1.

`m_1* m_2=-1`

`-(3)/(4)* m_2=-1`

`m_2=(4)/(3)`

The point slope form of a line is

`y-y_1=m(x-x_1)`

where, m is slope.

The slope of new line is
`(4)/(3)` and it passes through P(-3,-15). So, the equation of line of new road is

`y-(-15)=(4)/(3)(x-(-3))`

`y+15=(4)/(3)(x+3)`

`y+15=(4)/(3)x+4`

Subtract 15 from both sides.

`y=(4)/(3)x+4-15`

`y=(4)/(3)x-11`

Therefore, the equation of the line representing the new road is
`y=(4)/(3)x-11`.