Question

Is 3x = 2y a linear equation?

Answer 1

Answer is Yes, it’s a linear equation

Reason - an equation is linear if the graph forms a straight line. This will happen when the highest power of x is 1 (with no exponents)

Step by step

I put the equation in slope intercept form
y = mx+b to solve and graph

2y = 3x

Divide both sides by 2 to solve for y

2/2 y = 3/2x

y = 3/2x + 0 (there is no y intercept so it is 0)

This gives us two point to graph

(0,0) and (2, 3)

* 3/2x is y/x so we know x=2, y=3 and
0 y intercept means the line will cross at 0,0

This confirms our answer that yes, it’s a straight linr

Answer 2

In order to be linear, the equation needs to be in the following form:

`y=mx+b`

Rewriting the equation 3x = 2y, we have:

`\begin{gathered} 2y=3x \\ y=(3x)/(2) \\ y=(3)/(2)x+0 \end{gathered}`

The equation can be written in the form y = mx + b (in this case, m = 3/2 and b = 0), so this is a linear equation.