Answer:
Equation of the perpendicular line: y = x - 7
Explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
Original equation: y = -x + 6
slope (m) = -1
y-intercept (b) = 6
The negative reciprocal of -1 is positive 1. Therefore, the slope of the line that is perpendicular to the original equation is 1.
And given the point, (7, 0), we can write the following linear equation for the second line that is perpendicular to the original equation:
Perpendicular line equation: y = x + b
Substitute (7, 0) into the equation to find the y-intercept:
y = x + b
0 = 1(7) + b
0 = 7 + b
- 7 = 7 + b - 7
- 7 = b
Therefore, the equation of the line that is perpendicular to y = -x + 6 is:
y = x - 7.