Question

How do you write a line through: (4-2), parallel to y=x+2?

Answer 1

Equation of parallel line through (4,-2) is

`color(maroon)(y = x - 6`

Explanation:

Standard form of slope-intercept equation is

`y = mx + c, " where m is the slope and c the y-intercept"`

Given equation is #y = x + 2"

Hence `Slope = m = 1`

`"Parallel line will also have the same slope m = 1"`

Having known slope and a point on the line, Equation for the same is

`(y - y_1 = m * (x - x_1)`

`y + 2 = 1 * (x - 4)`

`color(maroon)(y = x - 4 - 2 = x - 6`

Answer 2

`y=x-6`

Explanation:

Parallel lines have the same slope (in this case, the slope is 1).

Slope-intercept form of a line: `y=mx+b` where `m` represents slope and `b` the y-intercept

`y=x+b rarr` This is our current equation (we don't know the y-intercept).

Let's plug in the point given to us: `(4, -2)`

`-2=4+b`

`b=-6 rarr` This is the y-intercept

Our equation is `y=x-6`