Question

choose the equation in point slope form for the line that is perpendicular to the given line and passing through the given point

Answer 1

We want to determine the equation in point slope form for the line that is perpendicular to the given line and passing through the point (5.6) .

The equation and the point is;

`y=(2)/(3)x+9,(5,6)`

We know that for two lines to be perpendicular, the product of their slopes should be -1.

Therefore, the slope of the perpendicular should be;

`m=-(1)/(((2)/(3)))=-(3)/(2)`

The second condition is that the line must pass through the point (5,6) , to do thid, we write the equation of the line in point slope form which is;

`y-y_1=m(x-x_{1_{}})`

Inserting all values, we have,

`y-6=.-(3)/(2)(x-5)`

That is the final answer.