Question

Is y + 4 = 2x linear ?

Answer 1

Yes, it is a linear equation.

Explanation:

Given:

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

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

where:

`m=2` (the slope), and the point `(x_1,y_1)` is `(0,-4)`.

The equation can be converted to slope-intercept form `(y=mx+b)` by solving for `y`.

`y+4=2x`

Subtract `4` from both sides.

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

`y=mx+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=2x` to the standard from :

`Ax + Bx=C`,

where `A and B` are coefficients, and `C` is the constant (has no coefficient).

`y+4=2x`

Subtract `4` from both sides.

`y=2x-4`

Subtract `2x` from both sides.

`y-2x=-4`

All of these linear equations will give the same graph.

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