Question

Consider the line -x+3y=1

Answer 1

The line
-x+3y=1 can be moved into slope intercept form to get slope.
slope is what matters for questions that asks about perpendicular/parallel...

isolate y to get slope intercept form


-x+3y=1
add x to both sides
3y = x + 1
divide both sides by 3
y = (x+1)/3
y = x/3 + 1/3

the slope is 1/3 because x/3 is the same as 1/3 * x.

the line that is perpendicular to this line has a slope that is the negative recirpocal of the original slope like.

perpendicular line slope: -3. (reciprocal of 1/3 is 3; then make that negative).

Told that this perp line passes through (7,-5), using slope intercept form y = mx + b with unknown y-intercept b value:

y = -3x + b

since (7,-5) means at x = 7, y = -5, plug those numbers in to solve for b

-5 = -3(7) + b
-5 = -21 + b
b = -5 + 21
b = 16

perpendicular line:
y = -3x + 16

for the parallel line has the same slope as the original
slope of parallel line: 1/3

we are told that parpall line goes through (7,-5) so using the unfinished slope-intercept form y = mx + b with unfinishe dinfo: we have

y = 1/3 x + b

since at x = 7 we have y = -5, plug it in

-5 = (1/3)(7) + b
-5 = 7/3 + b
b = -5 - 7/3
b = -15/3 - 7/3 .... same denominator for fraction add/subtract
b = -22/3

parallel line equation:
y = 1/3x - 22/3