The following line passes through point (X1, Y1)
:
y = fractionReduce( SLOPE_NUMERATOR, SLOPE_DENOMINATOR ) x + b
What is the value of the y
-intercept b
?
(Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR) / SLOPE_DENOMINATOR
Substituting (X1, Y1)
into the equation gives:
Y1 = fractionReduce( SLOPE_NUMERATOR, SLOPE_DENOMINATOR ) \cdot X1 + b
Y1 = fractionReduce( X1*SLOPE_NUMERATOR , SLOPE_DENOMINATOR ) + b
b = Y1 - fractionReduce( X1*SLOPE_NUMERATOR , SLOPE_DENOMINATOR )
b = fractionReduce( Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR, SLOPE_DENOMINATOR )
Plugging in fractionReduce( Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR, SLOPE_DENOMINATOR )
for b
, we get y = fractionReduce( SLOPE_NUMERATOR, SLOPE_DENOMINATOR ) x + fractionReduce(Y1*SLOPE_DENOMINATOR-X1*SLOPE_NUMERATOR,SLOPE_DENOMINATOR)
.