Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 Please show all of your work.

This method will use y = mx + b to find the equation
instead of the point-slope method.

We are being asked to
find the equation of a line perpendicular to -9x -2y = 10 that passes through the point
(-9,9).

We will first find the slope of the perpendicular
line by transforming the given equation into slope-intercept form which is y = mx +
b.

-9x-2y = 10

-2y = 9x +
10

y = -9/2x - 5

The slope of
a line perpendicular to the given equation will be 2/9 which is the "opposite
reciprocal" of -9/2.

Now we will use direct substitution
into y = mx +b to find the y intercept of the new
equation.

y = mx + b

9 =
2/9(-9) + b

9 = -2 + b

11=
b

Now, write the equation in slope-intercept form using the
slope 2/9 and the y intercept 11.

The
equation of the line that is perpendicular to the given line and containing the given
point is y = (2/9)x + 11.