Question

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1).

Answer 1

This is more of a math based question, so to find the equation of a line, one important thing to calculate is the slope. First, find the slope of the line given originally. 3x + y = 7 --> y = 7 - 3x --> slope = m = -3.
Next, the slope of a perpendicular is the negative inverse, so in this case it would be 1/3.
Given the slope, we can calculate the equation using the point-slope form which is y-y_1=m(x-x_1) where y_1 and x_1 are the y and x coordinates of a point on that line. Thus, using the point (6, -1), we can substitute in and get y-(-1) = 1/3(x-6) --> y + 1 = x/3 - 2--> y = x/3 -1 as your final answer. I hope that was helpful :)