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;

$y=\frac{2}{3}x+9,(5,6)$

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;

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

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,

$y-6=.-\frac{3}{2}(x-5)$

That is the final answer.