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)?a. y = -1/3x + 3b. y = -1/3x + 7c. y = 3x - 13d. y = 3x + 5

Answer 1

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

Explanation:

Straight lines are set out in the format of
`y = mx+c`, where
`m` is the gradient, and
`c` is the y-intercept.

The gradient between parallel lines remains the same, and this means the gradient of the new line will also be
`-(1)/(3)`.

This rules out options C and D.

Going back to the format, so far, we have filled in
`y=-(1)/(3)x+c`. We are still looking for the y-intercept.

We can find that using the coordinate you've been given,
`(6,5)`.

This coordinate tells us that when
`x=6`,
`y=5`. Therefore we can substitute those in the places of
`x` and
`y` in the original equation.

This leaves us with
`5 = -(1)/(3)(6)+c`.

We can now rearrange for
`c`.

`5 = -2 + c\\c=7`

Now we have all the values we need, we can form the final equation.

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

This indicates the answer is option B. Hope this helps.