Final answer:
To find the equation of the line perpendicular to the given line and passing through the point (10, -13), calculate the negative reciprocal of the given line’s slope and use the point-slope form. The equation is y = -5x + 37.
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to another line, and that passes through a given point (10, -13). First, we need to find the slope of the given line by rearranging its equation into slope-intercept form (y = mx + b). The equation given is (x - 5y)/4 = (x - 1)/2. Solving for y, we get:
- 2(x - 5y) = 4(x - 1)
- 2x - 10y = 4x - 4
- 10y = 2x - 4
- y = (2x/10) - (4/10)
- y = (1/5)x - 2/5
The slope of this line is 1/5. Perpendicular lines have slopes that are negative reciprocals. Therefore, the slope of the perpendicular line is -5 (the negative reciprocal of 1/5). Using the point-slope form of the equation of a line, which is (y - y1) = m(x - x1), and the point (10, -13), the equation of the line is:
y - (-13) = -5(x - 10)
Simplifying this, we get:
y + 13 = -5x + 50
y = -5x + 37
This is the equation of the line that is perpendicular to the given line and passes through the point (10, -13).