Question

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

Parallel lines have the same slope. The slope of y = -1/3 x + 4 is -1/3.

The equation is

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

y = -1/3 x -1/3 (- 6) + 5 = -1/3 x + 2 + 5 = -1/3 + 7

The equation is: y = - 1/3 x + 7

y = -1/3 x

Answer 2

`y = -(1)/(3) x + 7`

Explanation:

Given: y =
`-(1)/(3) x + 4` and passes through the point (6, 5).

Here we have to find the equation of the line that is parallel to the given line.

If the two lines are parallel, then their slopes must be the same.

From the given equation, the slope(m) =
`-(1)/(3)`

So the slope of the parallel line also will be the same.

Now we have to find the y-intercept of the parallel line.

The general form of slope-intercept form y = mx + b, where "m" is the slope and "b" is the y-intercept.

We know m =
`-(1)/(3)` and it is passes through the point (6, 5)

Here x = 6 and y = 5

Now plug in these values in the above slope-intercept and find the y-intercept.

5 =
`-(1)/(3) *6 + b`

5 = -2 + b

Adding 2 on both sides, we get

b = 5 + 2

b = 7

Now we got slope (m) = -1/3 and y-intercept(b) = 7

So the required equation is y =
`-(1)/(3) x + 7`