Question

Question #cfb72

Answer 1

`y=2/7x+1`

Explanation:

To write an equation for a line, we are going to use the slope and y-intercept.

Looking at the equation of the existing line: `y = 2/7 x -3`, we see that it is in slope-intercept form ( `y=mx+b` ) where `m`, the slope, is `2/7`.

We're looking for a line that is parallel to this line; for this second line to be parallel, it must have the same slope.

If we know both the slope and a point that the line goes through, we can find the y-intercept.

Starting with:
`y=mx+b`

Substitute our slope, `color(orange)[2/7]`:
`y=color(orange)[2/7]x+b`

And our point, `(color(green)7,color(blue)3)`:
`color(blue)3=2/7*color(green)7+b`

Now we can simplify - first cancel out the 7s:
`3 = 2 + b`

Subtract both sides by 2:
`3 - 2 = b`
`1 = b`

Now we have all the information we need to write an equation for our new line. To write the equation for this line, we can use the familiar slope-intercept form.

Starting with our formula:
`y=mx+b`

Substitute our slope, `color(orange)[2/7]` and y-intercept `b`, `color(purple)1`:
`y=color(orange)[2/7]x+color(purple)1`

...and we're done!

It's always good to double check our work - one way to do that is to graph both equations. We can also plug our `(x,y)` of `(color(green)7,color(blue)3)` into our equation to make sure it actually passes through that point (since we're confident that our slope is correct). If we do that and simplify, we'll see that:
`color(blue)3=2/7*color(green)7+1`
`3 = 2+1`
`3 = 3` ✓