7 x+8 y=6 y-8

Step 2 of 2: Find the equation of the line which passes through the point $(-9,2)$ and is perpendicular to the given line. Express your answer in slope-intercept form. Simplify your answer.

Step 1 ：First, solve the given equation for y to find the slope of the line. The equation is 7x + 8y = 6y - 8. Simplifying this gives y = -\(\frac{7}{2}\)x - 4. The slope of this line is \(\frac{2}{7}\).

Step 2 ：The slope of a line perpendicular to this line will be the negative reciprocal of this slope. So, the perpendicular slope is -\(\frac{7}{2}\).

Step 3 ：Next, use the point-slope form of a line to find the equation of the line that passes through the point (-9,2) and is perpendicular to the given line. This gives the equation y - 2 = -\(\frac{7}{2}\)x - \(\frac{63}{2}\).

Step 4 ：Solving this equation for y gives y = -\(\frac{7}{2}\)x - \(\frac{59}{2}\).

Step 5 ：Final Answer: The equation of the line which passes through the point (-9,2) and is perpendicular to the given line is \(\boxed{y = -\frac{7}{2}x - \frac{59}{2}}\).