Question

What is the equation of the line perpendicular to

x−5y=15 that passes through the point (−2,5)?
a) y= 1/5x −3
b) y=−1/5 x−3
c) y=5x+3
d) y=−5x+3

Answer 1

The equation of the line perpendicular to x - 5y = 15 and passing through the point (-2, 5) is y = -5x + 3.

Step-by-step explanation:

The equation of the line perpendicular to x - 5y = 15 that passes through the point (-2, 5) can be found using two main steps: finding the slope of the given line and using the point-slope form to find the equation of the perpendicular line. First, rearrange the given equation into slope-intercept form: y = mx + b, where m is the slope. Given equation in slope-intercept form is y = 1/5x - 3, the slope of the line is 1/5. A line perpendicular to this will have a slope that is the negative reciprocal, so the slope of the perpendicular line will be -5. Now use the point-slope form with the given point (-2, 5) and the slope -5: y - y1 = m(x - x1), which simplifies to y = -5x + 3.