Question

What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) ? Enter your answer in the box.

Answer 1

Find slope: parallel lines have same slope

−x+3y=6
+x +x
----------------
3y=x+6
3/3y=x/3+6/3
y=1/3x+2

Slope=1/3

Use slope and point (3, 5) to find b, y- intercept
y=mx+b
(5)=(1/3)(3)+b
5=1+b
5-1=1-1+b
4=b

Now we put it all together using m=1/3 and b=4
y=1/3x+4

Answer 2

The equation of a line parallel to −x+3y=6 and passes through the point (3, 5) is; 3y - x = 12

Parallel lines have equal slopes;

m1 = m2

The line −x+3y = 6 can be rewritten as;

y = (1/3)x +2 and has slope, m1 = 1/3

Therefore; since parallel lines have equal slope;

m1 = m2

The equation of the required line which passes through the point (3, 5) and has slope, -3 is therefore;

• 1/3 = (y - 5)/(x-3)

By cross product;

• 3y -15 = x - 3

• 3y = x + 12

• 3y - x = 12

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