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

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 : .

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

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

We have,

Slope of this line is and y-intercept is 7.

Product of slopes of two perpendicular line is -1.

The point slope form of a line is

where, m is slope.

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

Subtract 15 from both sides.

Therefore, the equation of the line representing the new road is .

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