Yes.
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Yes, y = -4x + 3 is a linear equation.
Yes, it is a linear straight line equation.
It is a linear equation in three variables which is equivalent to a linear equation in two variables. This is because 3 + e = 2.3f +e - 7g is equivalent to 3 = 2.3f -7g
The equation is linear and so has no vertex.
You cannot solve one linear equation with two variables.