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

Apr 11, 2018

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

color(maroon)(y = x - 6

#### Explanation:

Standard form of slope-intercept equation is

$y = m x + c , \text{ where m is the slope and c the y-intercept}$

Given equation is y = x + 2"

Hence $S l o p e = m = 1$

$\text{Parallel line will also have the same slope m = 1}$

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

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

$y + 2 = 1 \cdot \left(x - 4\right)$

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

Apr 11, 2018

$y = x - 6$

#### Explanation:

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

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

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

Let's plug in the point given to us: $\left(4 , - 2\right)$

$- 2 = 4 + b$

$b = - 6 \rightarrow$ This is the y-intercept

Our equation is $y = x - 6$