Write the equation of a line that is perpendicular to y=7/5x+ 6 and that passes through the point (2,-6).

Given that,

The equation of line is y=7/5x+ 6 and that passes through the point (2,-6).

To find,

The equation of line that is perpendicular to the given line.

Solution,

The given line is :

y=7/5x+ 6

The slope of this line = 7/5

For two perpendicular lines, the product of slopes of two lines is :

Equation will be :

y=-5x/7+ b

Now finding the value of b. As it passes through (2,-6). The equation of line will be :

So, the required equation of line is :

y=-5x/7+ (-32/7)