Answer:
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. This means that when you multiply the slopes of the perpendicular lines, its product = -1.
Given the linear equation, y = -9x - 1, and the point, (-3, 7):
Since the slope of the given linear equation is: m1 = -9, then it means that the slope of the other line (m2) = 1/9:
m1 × m2 = -1
-9 × 1/9 = -1
Next, we need to find the y-intercept of the other line. The y-intercept is the point on the line where it crosses the y-axis, and has coordinates (0, <em>b</em>). It is also the value of the y-coordinate when its corresponding x-coordinate = 0.
Using the given point, (-3, 7), and the slope of the other line, m2 = 1/9:
We need to substitute these values into the slope-intercept form, y = mx + b, to solve for the y-intercept, (b):
y = mx + b
7 = 1/9(-3) + b
7 = -1/3 + b
Add 1/3 to both sides of the equation to solve for b:
7 + 1/3 = 1/3 -1/3 + b
22/3 = b
Therefore, the y-intercept (b) = 22/3.
The linear equation of the other line is: y = 1/9x + 22/3
