Answer:
Perpendicular line: y = ⅕x + 0 or y = ⅕x
Step-by-step explanation:
Given the point, (10, 2), and the linear equation, y = -5x + 7:
In order to find the equation of the perpendicular line that passes through (10, 2), we must first determine the definition of perpendicular lines.
Definition:
Perpendicular lines have negative reciprocal slopes ⇒ this means that when you take and multiply the slopes of both lines, it results in a product of -1.
- In other words, since the slope of the given line, y = -5x + 7 is m₁ = -5, then it means that the slope of the other line must be m₂ = ⅕ because:
m₁ × m₂ = -1
-5 × ⅕ = -1
Solution:
Now that we have the slope of the other line, m₂ = ⅕, and the given point, (10, 2), substitute these values into the slope-intercept form to solve for the y-intercept, b :
y = mx + b
2 = ⅕(10) + b
2 = 2 + b
Subtract 2 from both sides:
2 -2 = 2 -2 + b
0 = b
Hence, the y-intercept is b = 0.
Equation:
The linear equation of the perpendicular line that passes through point (10, 2) is: y = ⅕x + 0 or y = ⅕x
