randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) -1 * A / B C / B

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!

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1 }); style({ stroke: BLUE, fill: BLUE }); plot(function( x ) { return x * SLOPE + Y_INTERCEPT; }, [ -10, 10 ]);
randRange(-5, 5) randRangeNonZero(-5, 5) randRange(1, 5) -A / B C / B

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
-A -B -C

`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!

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1 }); style({ stroke: BLUE, fill: BLUE }); plot(function( x ) { return x * SLOPE + Y_INTERCEPT; }, [ -10, 10 ]);