# Is y + 4 = 2x linear ?

Feb 27, 2018

Yes, it is a linear equation.

#### Explanation:

Given:

$y + 4 = 2 x$ is in the point-slope form for a linear equation:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$,

where:

$m = 2$ (the slope), and the point $\left({x}_{1} , {y}_{1}\right)$ is $\left(0 , - 4\right)$.

The equation can be converted to slope-intercept form $\left(y = m x + b\right)$ by solving for $y$.

$y + 4 = 2 x$

Subtract $4$ from both sides.

$y = 2 x - 4$ is in slope-intercept form:

$y = m x + b$,

where:

$m$ is the slope ($2$), and $b$ is the y-intercept (value of $y$ when $x = 0$.

We can also convert $y + 4 = 2 x$ to the standard from :

$A x + B x = C$,

where $A \mathmr{and} B$ are coefficients, and $C$ is the constant (has no coefficient).

$y + 4 = 2 x$

Subtract $4$ from both sides.

$y = 2 x - 4$

Subtract $2 x$ from both sides.

$y - 2 x = - 4$

All of these linear equations will give the same graph.

graph{y=2x-4 [-10, 10, -5, 5]}