What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?

Answer 1

Lines that are parallel have the same slope. Therefore the line of the equation that you are finding has the slope = -1/3 and we now have y=-1/3x +b for the unknown equation so far.

Using the point which the line must pass (6,5), we can plug x and y into the unknown equation to solve for b, the y-intercept.

5=-1/3(6)+b

5=-2+b

7=b

The equation of the line parallel to the given line is y = -1/3 x +7

Answer 2

If your line is parallel to the given equation, then you know the slope of the line is going to be the same.

So if the slope of the given equation is -1/3, then -1/3 will be the m for your second equation.

So now you have two key factors:

1) the slope (m) = -1/3

2) a point on the line = (6,5)

It would make the most sense to now use Point-Slope Form y-y₁=m(x-x₁)

Plug in and then solve the equation for y

-1/3 for m

6 for x₁

5 for y₂

y-5=-1/3(x-6)

y-5=-1/3x+2

+5 +5

y= -1/3x+7