Khan/khan-exercises

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 Converting between slope intercept and standard form
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( -3, 3 ) randRangeNonZero( -3, 3 ) SLOPE <= 0 ? -1 * SLOPE : SLOPE SLOPE <= 0 ? 1 : -1 SLOPE <= 0 ? Y_INTERCEPT: -1 * Y_INTERCEPT

Convert the following equation from slope intercept form to standard form.

In other words, if the equation is rewritten to look like Ax + By = C, what are the values of A, B, and C?

Assume A is positive.

y = expr([ "+", [ "*", SLOPE, "x" ], Y_INTERCEPT ])

A B C
A -B -C

A =

B =

C =

Move the x term to the same side as the y term.

expr([ "*", -SLOPE, "x" ]) + y = Y_INTERCEPT

Since the slope is 0 and there is no x term, the equation is already in slope intercept form.

y = Y_INTERCEPT

Multiply both sides by -1 so that A will be positive

expr([ "*", SLOPE, "x" ]) - y = -Y_INTERCEPT

Inspecting the equation in standard form, we see the following.

\begin{align*}A &= A\\ B &= B\\ C &= 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 ]);
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