The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
What is the isolation of a variable in an equation?
Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.
Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.
How to solve the question?
In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.
This means that we need to isolate the variable m, to get an expression equal to m.
The isolation of the variable m can be done as follows:
y = mx + b,
or, y - mx = mx + b - mx {Subtracting mx from both sides},
or, y - mx = b {Simplifying},
or, y - mx - y = b - y {Subtracting y from both sides},
or, -mx = b - y {Simplifying},
or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}
or, m = (y - b)/x {Simplifying}.
Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
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