Answer:
y = 9x - 53
Explanation:
Relationship between the slopes of perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other, as shown by the formula m2 = -1/m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we're given.
Identifying the slope of y = -1/9x + 5:
y = -1/9x + 5 is in the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where
- m is the slope
- and b is the y-intercept.
Thus, the slope (i.e., m1) is -1/9.
Determining the slope of the other line:
Now we can find the slope of the other line (i.e., m2) by substituting -1/9 for m1 in the perpendicular slope formula:
m2 = -1 / (-1/9)
m2 = -1 * -9/1
m2 = 9
Thus, the slope of the other line is 9.
Finding the y-intercept of the other line:
Now we can find the y-intercept (b) of the other line by substituting 9 for m and (7, 10) for (x, y) in the slope-intercept form:
10 = 9(7) + b
(10 = 63 + b) - 63
-53 = b
Thus, the y-intercept of the other line is -53.
Writing the equation of the other line in slope-intercept form:
Therefore, y = 9x - 53 is the equation of the line perpendicular to y = -1/9x + 5 and passing through the point (7, 10) in slope-intercept form: