Find the equation of the line parallel to the line 3x + y = 5 and containing the point (4, – 2).

Answer 1

y=-3x+5

When lines are parallel with one another, they must have the same slope. Otherwise one line would cross the other because of the difference in steepness. They also can't be overlapping one another, so they have to cross the y axis at a different place.

Therefore, the -3x would have to be the slope of the parallel line and the y-intercept could NOT also be 5, otherwise the two lines would be overlapping.

So we have:
y=-3x+b

Plug in x and y from the given point:
-2=-3(4)+b

Solve for b, replace the 4 and -2 back to x and y, and you have the equation of the line parallel to the line 3x+y=5 and containing the point (4, -2).

Answer 2

Got it Thanks!