Yes, generelly if there are no exponents greater than 1, it is a linear equation.
in this case you can rearrange the equation to be:
4x-5y=10 ==> 4x-10 = 5y ==> 4/5x-2=y
y=mx+b
m=slope
b=y-intercept
slope = 4/5
y-intercept = -2
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It is a linear equation in the single variable, m. It has the solution m = 0
5a - 10 = 4a + 8 is a linear equation in one variable.
It is a linear equation in x. It has a solution, which is x = -5
Yes, because no term has an exponent (power) other than 1.