# How do you write the equation of a line in slope intercept, point slope and standard form given (4,2) parallel to y=2x+3?

Feb 27, 2016

$\left(y - 2\right) = 2 \left(x - 4\right)$ (in point slope forms) or $y = 2 x - 6$ (in slope intercept form) or $2 x - y - 6 = 0$ (in standard form).

#### Explanation:

The equation of a line in slope intercept form is given as $y = m x + c$, where $m$ is the slope of line and $c$ is intercept formed by it on $y$-axis.

Point slope form is used to give equation of a line passing through a given point, say $\left({x}_{1} , {y}_{1}\right)$ and slope $m$. It is written as $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$.

Standard form of equation is in the form $a x + b y + c = 0$.

In the given equation, $y = 2 x + 3$ is already in slope-intercept form and its slope is $2$. Slope of any line parallel to it will also be $2$.

To find the equation of a line passing through $\left(4 , 2\right)$ with a slope of $2$, we use point slope form ad the equation is given by

$\left(y - 2\right) = 2 \left(x - 4\right)$ or $y - 2 = 2 x - 8$ or $y = 2 x - 6$ (in slope intercept form) or $2 x - y - 6 = 0$ (in standard form).