Answer:
y=9x - 53
Explanation:
To find the equation of the line that passes through the point (7, 10) and is perpendicular to the line y = (-1/9)x - 9, you'll want to determine the slope of the perpendicular line. The slope of the original line is -1/9.
For a line that is perpendicular, the negative reciprocal of the slope is used. So, the slope of the perpendicular line is 9/1, which is just 9.
Now that you have the slope (m = 9) and the point (7, 10), you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substitute the values (x1, y1) = (7, 10) and m = 9:
y - 10 = 9(x - 7)
Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):
y - 10 = 9x - 63
Add 10 to both sides:
y = 9x - 53
So, the equation of the line that passes through (7, 10) and is perpendicular to the line y = (-1/9)x - 9 is:
y = 9x - 53.