The equation y = mx + b is used to express the equation of a line. Which solution is a correct way to solve this equation for x in terms of y?
A) y = mx + b
B) y – b = mx
C) y – b/m = x
D) y/m – b = x
The equation y = mx + b is used to express the equation of a line. Which solution is a correct way to solve this equation for x in terms of y?
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The correct answer is C) y – b/m = x.
To solve the equation ( y = mx + b ) for ( x ), follow these steps:
1. Start with the original equation:
( y = mx + b )
2. Subtract ( b ) from both sides:
( y – b = mx )
3. Divide both sides by ( m ) to isolate ( x ):
( x = frac{y – b}{m} )
This can be rearranged to ( y – b/m = x ) by restructuring the relationship, but this requires clarification that the division by ( m ) comes after subtracting ( b ) from ( y ).
So, restating accurately:
( x = frac{y – b}{m} )
This means option C is phrased correctly in terms of positioning, but option C should rather present as: ( x = (y – b)/m ).
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