Question

Write the standard form equation of the line parallel to y = 2x – 1 that contains the point (2,-7)

Answer 1

`y=2x+3`

Explanation:

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

`y=mx+b`

Using the slope-intercept form, the slope is 2.

`m=2`

So in order for us to find an equation that is parallel, the slopes must be equal. We need to find the parallel line using the point-slope formula.

We use the slope 2 and a given point
`(2,7)` to substitute for x1 and y1 in the point-slope form
`y-y^1 = m (x-x^1)`, which is derived from the slope equation:
`m=(y2-y1)/(x2-x1)`

Now we simplify the equation and keep it in point-slope form.

`y-7=2` ×
`(x-2)`

Simplify
`2` ×
`(x-2)`

`y-7=2x-4`

`Rewrite.~y-7=0+0+2~x~(x-2)`

`Simplify~ by~adding~zeros.~y-7=2 ~x~(x-2)`

`Apply~the~distributive~property.~y-7=2x+2~X~-2`

`Multiply~2~by~-2.~y-7=2x-4`

Last, We move all terms not containing y to the right side of the equation.

Add 7 to both sides of the equation.

`y=2x-4+7`

Add −4 and 7 and your answer will be:
`y=2x+3`