Question

Question #7a474

Answer 1

The answer is `y=3x+10`

Explanation:

Since it is parallel, it has the same slope. You now know the equation of the line is

`y=3x+b`

You are given a point on the line, so plug that in:

`7=3*(-1)+b`

`7=-3+b`

`b=10`

The answer is `y=3x+10`! Yay!

Answer 2

The equation of the line that is parallel to the given line is
`y = 3 x + 10`

Explanation:

Parallel lines have the same slopes as each other.
The only difference between them is `b` -- the `y` intercept.

If they had even the same `y` intercept as well as the same slope, they wouldn't be parallel lines -- they would be the SAME line!

So to find the equation of the line parallel to the given line:

• Find the slope `m` of the parallel line
• Find the `y`-intercept `b` of the parallel line

Find the slope `m` of the parallel line

The slopes of parallel lines are the same as each other.
The slope of the given line is `3`, so the slope of the parallel line is also `3`

So the equation of the parallel line so far is
`y = mx + b`
`y =  3 x + b`

`color(white)(mmmmmm)`. . . . . . . . . . . . . . . . . . . .

Find the `y` intercept `b` of the parallel line

The slope-intercept formula of a line is
`y = mx + b`
where `b` is the `y` intercept.

This formula has four unknowns, but you know three of them.
`y = 7` (from the given ordered pair)
`m = 3` (same slope as the given line)
`x = - 1` (from the same given ordered pair
`b` `"----"` Find `b`

1) Sub in the values for the letters of the formula and solve for `b`
`y =  m   x  + b`
`7 = (3)`(-`1`) `+ b`

2) Clear the parentheses by distributing the `3`
`7= - 3 + b`

3) Add `3` to both sides to isolate `b`, defined as "the `y` intercept"
`10 = b`, the `y` intercept of the parallel line

`color(white)(mmmmmm)`. . . . . . . . . . . . . . . . . . . .

Now you can write the complete equation of the parallel line
`y = mx +   b`
`y =  3 x + 10` `larr` answer