If y = mt + c, how do you isolate m?

To isolate the variable ( m ) in the equation ( y = mt + c ), the goal is to rearrange the equation so that ( m ) is on one side by itself.

Starting from ( y = mt + c ), the first step is to eliminate ( c ) from the right side. This can be accomplished by subtracting ( c ) from both sides, leading to the equation ( y - c = mt ).

Next, to solve for ( m ), it is necessary to isolate ( m ) by dividing both sides of the equation by ( t ). This yields the equation ( m = \frac{y - c}{t} ).

Thus, the correct adjustment provides ( m ) as a function of ( y ), ( c ), and ( t ). The expression ((y - c)/t) succinctly represents the isolated form of ( m ), making this option the correct answer.

This approach effectively demonstrates how algebraic manipulation can be used to isolate a desired variable in an equation.