A =
B =
C =
Convert the following equation from standard form to slope intercept form.
In other words, if the equation is rewritten to look like y = mx + b, what are the values of m and b?
expr([ "*", A, "x"]) + expr([ "*", B, "y" ]) = C
m = SLOPE
b = Y_INTERCEPT
Move the x term to the other side of the equation.
expr([ "*", B, "y" ]) = expr([ "*", -1 * A, "x"]) + C
Divide both sides by B.
y = fractionReduce( -1 * A, B)-x + fractionReduce( C, B )
Inspecting the equation in slope intercept form, we see the following.
\begin{align*}m &= fractionReduce( -1 * A, B)\\
b &= fractionReduce( C, B )\end{align*}
Behold! The magic of math, that both equations could represent the same line!
Convert the following equation from slope intercept form to standard form.
y = coefficient(fractionReduce(-A, B))x +
fractionReduce(C, B)
In other words, what are the values of
A, B, and C
if the equation is rewritten to look like
\blue{A}x + \green{B}y = \pink{C}?
Note that A, B, and C should be integers.
A =
B =
C =
Move the x term to the same side as the y term.
coefficient(fractionReduce(A, B))x + y = fractionReduce(C, B)
To get integers, multiply all the terms by B.
coefficient(A)x +
By = C
Since the slope is 0 and there is no x term, the equation is already in slope intercept form.
y = Y_INTERCEPT
So we have \blue{A}
lot of
lots of
x, \green{B}
lot of
lots of
y, and a \pink{C}.
\blue{A}x + \green{B}y = \pink{C}
\begin{align*}
\blue{A} &= \blue{A}\\
\green{B} &= \green{B}\\
\pink{C} &= \pink{C}\end{align*}
Behold! The magic of math, that both equations could represent the same line!