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 ]);

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`

= `A`

`B`

= `B`

`C`

= `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 ]);