Question 941934

the line passing through the point ({{{6}}}, {{{9}}}) and the {{{center}}} ({{{h}}},{{{k}}}) of the circle {{{(x -4)^2 + (y -6)^2 = 36}}}

since {{{(x -4)^2 + (y -6)^2 = 36}}} we know that {{{h=4}}} and {{{k=6}}} (recall the circle formula {{{(x -h)^2 + (y -k)^2 = r^2}}} )

so, we have two points the point ({{{6}}}, {{{9}}}) and the point ({{{4}}}, {{{6}}}) 

now find equation of a line passing through these two points:

*[invoke change_this_name10094 6, 9, 4, 6]

since equation is {{{y=1.5*x}}} which is  {{{y=(3/2)x}}}; so, the slope is {{{3/2}}}